Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11927078 | C2 | semidirect |
| 2. C2×C4×D76 | C2 | semidirect |
| 3. #11926880 | C2 | semidirect |
| 4. #11926863 | C2 | semidirect |
| 5. #11926845 | C2 | semidirect |
| 6. #11926760 | C2 | semidirect |
| 7. #11926697 | C2 | semidirect |
| 9. C4×#64516 | C2 | semidirect |
| 10. C4×D152 | C2 | semidirect |
| 11. C19×#431 | C2 | semidirect |
| 24. #10597321 | C22 | semidirect |
| 29. C4×D76 | C22 | semidirect |
| 31. #10597316 | C22 | semidirect |
| 32. C4×Dic38 | C22 | semidirect |
| 33. C19×C4⋊C8 | C22 | semidirect |
| 36. C4×C8×C19 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. #10597275 | C22 | semidirect |
| 41. #10597274 | C22 | semidirect |
| 42. #10597273 | C22 | semidirect |
| 145. #431 | D19 | semidirect |
| 175. C4⋊C8 | C2×D19 | semidirect |
| 182. C4×C8 | C2×D19 | semidirect |
| 183. C19 | #3105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| C2×C4×D76 | 2 |
| #11926880 | 2 |
| #11926863 | 2 |
| #11926845 | 2 |
| #11926760 | 2 |
| #11926697 | 2 |
| #11926680 | 2 |
| C4×#64516 | 2 |
| C4×D152 | 2 |
| C19×#431 | 2 |
| #3105 | 19 |