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. #27133192 | C2 | semidirect |
| 2. #27133065 | C2 | semidirect |
| 3. #27133017 | C2 | semidirect |
| 4. #27132901 | C2 | semidirect |
| 6. #27132889 | C2 | semidirect |
| 7. Q16×Dic191 | C2 | semidirect |
| 8. SD16×Dic191 | C2 | semidirect |
| 9. D8×Dic191 | C2 | semidirect |
| 10. C4×C8×D191 | C2 | semidirect |
| 11. #495×C191 | C2 | semidirect |
| 118. C191 | #3168 | semidirect |
| 122. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133192 | 2 |
| #27133065 | 2 |
| #27133017 | 2 |
| #27132901 | 2 |
| #27132896 | 2 |
| #27132889 | 2 |
| Q16×Dic191 | 2 |
| SD16×Dic191 | 2 |
| D8×Dic191 | 2 |
| C4×C8×D191 | 2 |
| #495×C191 | 2 |
| #3168 | 191 |