Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#64545 | C2 | semidirect |
| 2. C2×#10597365 | C2 | semidirect |
| 3. #11927057 | C2 | semidirect |
| 4. #11926705 | C2 | semidirect |
| 5. #11926694 | C2 | semidirect |
| 6. #11926692 | C2 | semidirect |
| 7. #11926683 | C2 | semidirect |
| 8. #11926680 | C2 | semidirect |
| 9. #11926539 | C2 | semidirect |
| 10. C22⋊C8×D19 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 18. C2×#64545 | C22 | semidirect |
| 23. C2×Q16×C19 | C22 | semidirect |
| 25. #10597392 | C22 | semidirect |
| 26. C2×#64527 | C22 | semidirect |
| 27. C2×#64527 | C22 | semidirect |
| 30. C2×D152 | C22 | semidirect |
| 31. C2×C8×D19 | C22 | semidirect |
| 32. #10597341 | C22 | semidirect |
| 35. #10597338 | C22 | semidirect |
| 38. C19×#103 | C22 | semidirect |
| 40. #10597292 | C22 | semidirect |
| 42. #10597278 | C22 | semidirect |
| 43. (C2×D19)⋊C8 | C22 | semidirect |
| 44. #10597266 | C22 | semidirect |
| 61. #64545 | D4 | semidirect |
| 144. C22×C19 | #135 | semidirect |
| 172. #451 | D19 | semidirect |
| 199. C2×Q16 | C2×D19 | semidirect |
| 214. #103 | C2×D19 | semidirect |
| 220. C19 | #3002 | semidirect |
| 333. C22 | #10597365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64545 | 2 |
| C2×#10597365 | 2 |
| #11927057 | 2 |
| #11926705 | 2 |
| #11926694 | 2 |
| #11926692 | 2 |
| #11926683 | 2 |
| #11926680 | 2 |
| #11926539 | 2 |
| C22⋊C8×D19 | 2 |
| C19×#451 | 2 |
| #3002 | 19 |