Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27133278 | C2 | semidirect |
| 2. #27133067 | C2 | semidirect |
| 3. #27133046 | C2 | semidirect |
| 4. #27133021 | C2 | semidirect |
| 5. #27132908 | C2 | semidirect |
| 6. #27132905 | C2 | semidirect |
| 8. #27132763 | C2 | semidirect |
| 9. C4×Dic764 | C2 | semidirect |
| 10. #27132617 | C2 | semidirect |
| 11. C4×D8×C191 | C2 | semidirect |
| 117. C191 | #3175 | semidirect |
| 128. C4×D8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133278 | 2 |
| #27133067 | 2 |
| #27133046 | 2 |
| #27133021 | 2 |
| #27132908 | 2 |
| #27132905 | 2 |
| #27132896 | 2 |
| #27132763 | 2 |
| C4×Dic764 | 2 |
| #27132617 | 2 |
| C4×D8×C191 | 2 |
| #3175 | 191 |