Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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. C4×Q8×D191 | C2 | semidirect |
| 3. #27132978 | C2 | semidirect |
| 4. #27132955 | C2 | semidirect |
| 5. #27132864 | C2 | semidirect |
| 6. #27132863 | C2 | semidirect |
| 7. #27132803 | C2 | semidirect |
| 8. #27132766 | C2 | semidirect |
| 9. #27132762 | C2 | semidirect |
| 10. #27132719 | C2 | semidirect |
| 11. #477×C191 | C2 | semidirect |
| 87. Dic382 | #41 | semidirect |
| 108. Q8×C191 | #41 | semidirect |
| 140. C191 | #3112 | semidirect |
| 146. #477 | D191 | semidirect |
| 231. Q8 | #15690288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133214 | 2 |
| C4×Q8×D191 | 2 |
| #27132978 | 2 |
| #27132955 | 2 |
| #27132864 | 2 |
| #27132863 | 2 |
| #27132803 | 2 |
| #27132766 | 2 |
| #27132762 | 2 |
| #27132719 | 2 |
| #477×C191 | 2 |
| #3112 | 191 |