Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10597321 | C2 | semidirect |
| 3. #11926928 | C2 | semidirect |
| 4. #11926899 | C2 | semidirect |
| 5. #11926767 | C2 | semidirect |
| 6. #11926760 | C2 | semidirect |
| 7. #11926702 | C2 | semidirect |
| 8. #11926697 | C2 | semidirect |
| 9. #11926685 | C2 | semidirect |
| 11. C19×#431 | C2 | semidirect |
| 21. C2×Dic76 | C22 | semidirect |
| 24. C2×#64516 | C22 | semidirect |
| 30. #10597321 | C22 | semidirect |
| 31. C4×D76 | C22 | semidirect |
| 33. #10597316 | C22 | semidirect |
| 34. C4×Dic38 | C22 | semidirect |
| 35. C19×C4⋊C8 | C22 | semidirect |
| 38. C4×C8×C19 | C22 | semidirect |
| 41. #10597273 | C22 | semidirect |
| 42. #10597273 | C22 | semidirect |
| 148. #431 | D19 | semidirect |
| 178. C4⋊C8 | C2×D19 | semidirect |
| 185. C4×C8 | C2×D19 | semidirect |
| 186. C19 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| C2×#10597321 | 2 |
| #11926928 | 2 |
| #11926899 | 2 |
| #11926767 | 2 |
| #11926760 | 2 |
| #11926702 | 2 |
| #11926697 | 2 |
| #11926685 | 2 |
| #11926680 | 2 |
| C19×#431 | 2 |
| #3211 | 19 |