Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #27133282 | C2 | semidirect |
| 2. #27133068 | C2 | semidirect |
| 3. #27133022 | C2 | semidirect |
| 4. #27132906 | C2 | semidirect |
| 5. #27132901 | C2 | semidirect |
| 7. #27132764 | C2 | semidirect |
| 8. Q16×Dic191 | C2 | semidirect |
| 9. D8×Dic191 | C2 | semidirect |
| 10. #27132617 | C2 | semidirect |
| 11. #495×C191 | C2 | semidirect |
| 117. C191 | #3175 | semidirect |
| 121. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133282 | 2 |
| #27133068 | 2 |
| #27133022 | 2 |
| #27132906 | 2 |
| #27132901 | 2 |
| #27132896 | 2 |
| #27132764 | 2 |
| Q16×Dic191 | 2 |
| D8×Dic191 | 2 |
| #27132617 | 2 |
| #495×C191 | 2 |
| #3175 | 191 |