Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Frattini | C22 | C23×D23 |
| Fitting | C4×D4×C23 | C2 |
| hypercenter | C4×D4 | D23 |
| hypocenter | C23 | #525 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67288 | C2 | semidirect |
| 2. C22×C4×D23 | C2 | semidirect |
| 3. C4×D4×C23 | C2 | semidirect |
| 4. #10625110 | C2 | semidirect |
| 5. #10625108 | C2 | semidirect |
| 6. C4×C22⋊D23 | C2 | semidirect |
| 7. C4×C22⋊D23 | C2 | semidirect |
| 8. #10625067 | C2 | semidirect |
| 9. #10625065 | C2 | semidirect |
| 10. #10625055 | C2 | semidirect |
| 11. #10625054 | C2 | semidirect |
| 12. #10625053 | C2 | semidirect |
| 13. #10625049 | C2 | semidirect |
| 14. C4×D92 | C2 | semidirect |
| 15. #10625043 | C2 | semidirect |
| 19. C22×C4×C23 | C22 | semidirect |
| 23. C2×C22⋊D23 | C22 | semidirect |
| 33. C2×C4×D23 | C22 | semidirect |
| 34. C2×Dic46 | C22 | semidirect |
| 35. C4⋊C4×C23 | C22 | semidirect |
| 37. C22⋊C4×C23 | C22 | semidirect |
| 38. C42×C23 | C22 | semidirect |
| 40. C22⋊Dic23 | C22 | semidirect |
| 45. (C2×D23)⋊C4 | C22 | semidirect |
| 46. (C2×D23)⋊C4 | C22 | semidirect |
| 47. C4⋊Dic23 | C22 | semidirect |
| 48. Dic23⋊C4 | C22 | semidirect |
| 49. Dic23⋊C4 | C22 | semidirect |
| 50. Dic23⋊C4 | C22 | semidirect |
| 51. Dic23⋊C4 | C22 | semidirect |
| 52. C4×Dic23 | C22 | semidirect |
| 85. C4×D23 | D4 | semidirect |
| 92. C22×C23 | #41 | semidirect |
| 103. C2×D23 | #41 | semidirect |
| 136. C4×D4 | D23 | semidirect |
| 138. C23 | #525 | semidirect |
| 157. C22×C4 | C2×D23 | semidirect |
| 163. C4⋊C4 | C2×D23 | semidirect |
| 173. C22⋊C4 | C2×D23 | semidirect |
| 175. C42 | C2×D23 | semidirect |
| 225. C22 | #67288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67288 | 2 |
| C22×C4×D23 | 2 |
| C4×D4×C23 | 2 |
| #10625110 | 2 |
| #10625108 | 2 |
| C4×C22⋊D23 | 2 |
| #10625067 | 2 |
| #10625065 | 2 |
| #10625055 | 2 |
| #10625054 | 2 |
| #10625053 | 2 |
| #10625049 | 2 |
| C4×D92 | 2 |
| #10625043 | 2 |
| #525 | 23 |