Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27132945 | C2 | semidirect |
| 3. C8×Dic382 | C2 | semidirect |
| 4. #27132414 | C2 | semidirect |
| 5. #27132409 | C2 | semidirect |
| 43. Dic382 | SD16 | semidirect |
| 62. C8×C191 | SD16 | semidirect |
| 79. C191 | #1666 | semidirect |
| 142. C8 | #15690275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132945 | 2 |
| #27132860 | 2 |
| C8×Dic382 | 2 |
| #27132414 | 2 |
| #27132409 | 2 |
| #27132407 | 2 |
| #492×C191 | 2 |
| #1666 | 191 |