Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133213 | C2 | semidirect |
| 2. #27133213 | C2 | semidirect |
| 3. #27133040 | C2 | semidirect |
| 4. #27133036 | C2 | semidirect |
| 5. #27133014 | C2 | semidirect |
| 6. #27133010 | C2 | semidirect |
| 7. #27132879 | C2 | semidirect |
| 8. #27132810 | C2 | semidirect |
| 9. #431×C191 | C2 | semidirect |
| 120. C191 | #3207 | semidirect |
| 130. #431 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| #27133040 | 2 |
| #27133036 | 2 |
| #27133014 | 2 |
| #27133010 | 2 |
| #27132879 | 2 |
| #27132810 | 2 |
| #431×C191 | 2 |
| #3207 | 191 |