Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×#123 | C2 |
| prime radical | #10625108 | C2 |
| hypercenter | #123 | D23 |
| hypocenter | C23 | #551 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#123 | C2 | semidirect |
| 3. D4×Dic23 | C2 | semidirect |
| 4. C2×(C2×D23)⋊C4 | C2 | semidirect |
| 5. #10625097 | C2 | semidirect |
| 6. #10625069 | C2 | semidirect |
| 7. #10625069 | C2 | semidirect |
| 8. #10625068 | C2 | semidirect |
| 9. #10625063 | C2 | semidirect |
| 10. #10625057 | C2 | semidirect |
| 11. #10625056 | C2 | semidirect |
| 12. #10625054 | C2 | semidirect |
| 13. (C22⋊D23)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D23 | C2 | semidirect |
| 15. #10625049 | C2 | semidirect |
| 22. C22×Dic23 | C22 | semidirect |
| 25. C2×Dic46 | C22 | semidirect |
| 26. C4⋊C4×C23 | C22 | semidirect |
| 27. C4⋊C4×C23 | C22 | semidirect |
| 29. C22⋊C4×C23 | C22 | semidirect |
| 30. C22⋊C4×C23 | C22 | semidirect |
| 33. C22⋊Dic23 | C22 | semidirect |
| 42. C4⋊Dic23 | C22 | semidirect |
| 43. C4⋊Dic23 | C22 | semidirect |
| 44. C4⋊Dic23 | C22 | semidirect |
| 45. C4⋊Dic23 | C22 | semidirect |
| 46. Dic23⋊C4 | C22 | semidirect |
| 47. Dic23⋊C4 | C22 | semidirect |
| 48. C4×Dic23 | C22 | semidirect |
| 49. C4×Dic23 | C22 | semidirect |
| 50. C4×Dic23 | C22 | semidirect |
| 116. #123 | D23 | semidirect |
| 126. C23 | #551 | semidirect |
| 143. C4⋊C4 | C2×D23 | semidirect |
| 144. C4⋊C4 | C2×D23 | semidirect |
| 157. C22⋊C4 | C2×D23 | semidirect |
| 158. C22⋊C4 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#123 | 2 |
| #10625108 | 2 |
| D4×Dic23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| #10625097 | 2 |
| #10625069 | 2 |
| #10625068 | 2 |
| #10625063 | 2 |
| #10625057 | 2 |
| #10625056 | 2 |
| #10625054 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C22⋊C4×D23 | 2 |
| #10625049 | 2 |
| #551 | 23 |