Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
338 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #27133062 | C2 | semidirect |
| 3. #27133042 | C2 | semidirect |
| 4. #27133033 | C2 | semidirect |
| 5. #27133031 | C2 | semidirect |
| 8. #27132768 | C2 | semidirect |
| 9. C4×#15690277 | C2 | semidirect |
| 102. C191 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133275 | 2 |
| #27133062 | 2 |
| #27133042 | 2 |
| #27133033 | 2 |
| #27133031 | 2 |
| #27132919 | 2 |
| #27132902 | 2 |
| #27132768 | 2 |
| C4×#15690277 | 2 |
| #27132619 | 2 |
| #541×C191 | 2 |
| #3177 | 191 |