Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. #27133268 | C2 | semidirect |
| 2. #27133062 | C2 | semidirect |
| 3. #27133039 | C2 | semidirect |
| 4. #27133029 | C2 | semidirect |
| 5. #27133027 | C2 | semidirect |
| 6. #27132914 | C2 | semidirect |
| 7. #27132897 | C2 | semidirect |
| 8. #27132773 | C2 | semidirect |
| 9. C4×#15690272 | C2 | semidirect |
| 10. #27132619 | C2 | semidirect |
| 11. #540×C191 | C2 | semidirect |
| 114. C191 | #3176 | semidirect |
| 117. #540 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133268 | 2 |
| #27133062 | 2 |
| #27133039 | 2 |
| #27133029 | 2 |
| #27133027 | 2 |
| #27132914 | 2 |
| #27132897 | 2 |
| #27132773 | 2 |
| C4×#15690272 | 2 |
| #27132619 | 2 |
| #540×C191 | 2 |
| #3176 | 191 |