Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133219 | C2 | semidirect |
| 3. #27133033 | C2 | semidirect |
| 4. #27133032 | C2 | semidirect |
| 5. #27133027 | C2 | semidirect |
| 6. #27133021 | C2 | semidirect |
| 7. #27132656 | C2 | semidirect |
| 8. #97×D191 | C2 | semidirect |
| 9. #490×C191 | C2 | semidirect |
| 90. C191 | #3135 | semidirect |
| 97. #490 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133219 | 2 |
| #27133211 | 2 |
| #27133033 | 2 |
| #27133032 | 2 |
| #27133027 | 2 |
| #27133021 | 2 |
| #27132656 | 2 |
| #97×D191 | 2 |
| #490×C191 | 2 |
| #3135 | 191 |