Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #27133198 | C2 | semidirect |
| 2. #27133047 | C2 | semidirect |
| 3. #27133020 | C2 | semidirect |
| 4. #27132905 | C2 | semidirect |
| 6. #27132893 | C2 | semidirect |
| 7. #27132757 | C2 | semidirect |
| 8. #27132750 | C2 | semidirect |
| 9. #27132745 | C2 | semidirect |
| 10. C4×C8×D191 | C2 | semidirect |
| 11. #499×C191 | C2 | semidirect |
| 118. C191 | #3168 | semidirect |
| 121. #499 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133198 | 2 |
| #27133047 | 2 |
| #27133020 | 2 |
| #27132905 | 2 |
| #27132900 | 2 |
| #27132893 | 2 |
| #27132757 | 2 |
| #27132750 | 2 |
| #27132745 | 2 |
| C4×C8×D191 | 2 |
| #499×C191 | 2 |
| #3168 | 191 |