Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4⋊Q8×D191 | C2 | semidirect |
| 3. #27133034 | C2 | semidirect |
| 4. #27133012 | C2 | semidirect |
| 5. #27132869 | C2 | semidirect |
| 6. #27132868 | C2 | semidirect |
| 7. #27132865 | C2 | semidirect |
| 8. #27132803 | C2 | semidirect |
| 9. #27132800 | C2 | semidirect |
| 10. #27132715 | C2 | semidirect |
| 11. #461×C191 | C2 | semidirect |
| 107. C4×D191 | SD16 | semidirect |
| 148. C191 | #3206 | semidirect |
| 157. #461 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133210 | 2 |
| C4⋊Q8×D191 | 2 |
| #27133034 | 2 |
| #27133012 | 2 |
| #27132869 | 2 |
| #27132868 | 2 |
| #27132865 | 2 |
| #27132803 | 2 |
| #27132800 | 2 |
| #27132715 | 2 |
| #461×C191 | 2 |
| #3206 | 191 |