Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
712 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#397 | C2 |
| hypercenter | #397 | D19 |
| hypocenter | C19 | #2812 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597328 | C2 | semidirect |
| 2. #11926473 | C2 | semidirect |
| 3. #11926462 | C2 | semidirect |
| 4. #11926461 | C2 | semidirect |
| 5. #11926459 | C2 | semidirect |
| 6. #11926454 | C2 | semidirect |
| 7. #11926453 | C2 | semidirect |
| 8. #11926399 | C2 | semidirect |
| 9. C19×#397 | C2 | semidirect |
| 14. C22×D76 | C22 | semidirect |
| 15. C2×C4⋊C4×C19 | C22 | semidirect |
| 23. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 26. C2×Dic19⋊C4 | C22 | semidirect |
| 28. C19×#95 | C22 | semidirect |
| 29. C19×#95 | C22 | semidirect |
| 30. C19⋊#95 | C22 | semidirect |
| 31. C19⋊#95 | C22 | semidirect |
| 37. C23×D19 | D4 | semidirect |
| 148. #397 | D19 | semidirect |
| 170. C2×C4⋊C4 | C2×D19 | semidirect |
| 183. #95 | C2×D19 | semidirect |
| 184. #95 | C2×D19 | semidirect |
| 185. C19 | #2812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597328 | 2 |
| #11926473 | 2 |
| #11926462 | 2 |
| #11926461 | 2 |
| #11926459 | 2 |
| #11926454 | 2 |
| #11926453 | 2 |
| #11926399 | 2 |
| C19×#397 | 2 |
| #2812 | 19 |