Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×#121 | C2 |
| hypercenter | #121 | D23 |
| hypocenter | C23 | #546 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67290 | C2 | semidirect |
| 2. C2×D4×D23 | C2 | semidirect |
| 3. C23×#121 | C2 | semidirect |
| 4. #10625110 | C2 | semidirect |
| 5. #10625108 | C2 | semidirect |
| 6. #10625108 | C2 | semidirect |
| 7. #10625106 | C2 | semidirect |
| 8. C4×C22⋊D23 | C2 | semidirect |
| 9. C2×(C2×D23)⋊C4 | C2 | semidirect |
| 10. #10625067 | C2 | semidirect |
| 11. #10625065 | C2 | semidirect |
| 12. #10625056 | C2 | semidirect |
| 13. #10625055 | C2 | semidirect |
| 14. (C22⋊D23)⋊C4 | C2 | semidirect |
| 15. C22⋊C4×D23 | C2 | semidirect |
| 19. C2×D4×C23 | C22 | semidirect |
| 20. C2×D4×C23 | C22 | semidirect |
| 21. C22×C4×C23 | C22 | semidirect |
| 25. C2×C22⋊D23 | C22 | semidirect |
| 26. C2×C22⋊D23 | C22 | semidirect |
| 27. C22×Dic23 | C22 | semidirect |
| 28. C22×Dic23 | C22 | semidirect |
| 33. C2×C4×D23 | C22 | semidirect |
| 34. C2×C4×D23 | C22 | semidirect |
| 35. C2×Dic46 | C22 | semidirect |
| 36. C4⋊C4×C23 | C22 | semidirect |
| 37. C22⋊C4×C23 | C22 | semidirect |
| 38. C22⋊C4×C23 | C22 | semidirect |
| 39. C22⋊Dic23 | C22 | semidirect |
| 40. C22⋊Dic23 | C22 | semidirect |
| 41. C22⋊Dic23 | C22 | semidirect |
| 45. (C2×D23)⋊C4 | C22 | semidirect |
| 46. (C2×D23)⋊C4 | C22 | semidirect |
| 47. (C2×D23)⋊C4 | C22 | semidirect |
| 48. (C2×D23)⋊C4 | C22 | semidirect |
| 49. Dic23⋊C4 | C22 | semidirect |
| 50. Dic23⋊C4 | C22 | semidirect |
| 51. Dic23⋊C4 | C22 | semidirect |
| 52. C4×Dic23 | C22 | semidirect |
| 77. C22⋊D23 | D4 | semidirect |
| 110. C2×D23 | #41 | semidirect |
| 138. #121 | D23 | semidirect |
| 145. C23 | #546 | semidirect |
| 158. C2×D4 | C2×D23 | semidirect |
| 159. C2×D4 | C2×D23 | semidirect |
| 165. C22×C4 | C2×D23 | semidirect |
| 169. C4⋊C4 | C2×D23 | semidirect |
| 180. C22⋊C4 | C2×D23 | semidirect |
| 181. C22⋊C4 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67290 | 2 |
| C2×D4×D23 | 2 |
| C23×#121 | 2 |
| #10625110 | 2 |
| #10625108 | 2 |
| #10625106 | 2 |
| C4×C22⋊D23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| #10625067 | 2 |
| #10625065 | 2 |
| #10625056 | 2 |
| #10625055 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C22⋊C4×D23 | 2 |
| #546 | 23 |