Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#20259298 | C2 | semidirect |
| 3. #27133002 | C2 | semidirect |
| 4. #27132996 | C2 | semidirect |
| 5. #27132982 | C2 | semidirect |
| 6. #27132918 | C2 | semidirect |
| 7. #27132912 | C2 | semidirect |
| 8. #27132824 | C2 | semidirect |
| 9. #27132802 | C2 | semidirect |
| 10. #27132625 | C2 | semidirect |
| 11. #451×C191 | C2 | semidirect |
| 14. C2×#15690274 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. #20259254 | C22 | semidirect |
| 33. #20259246 | C22 | semidirect |
| 34. #20259246 | C22 | semidirect |
| 35. #20259244 | C22 | semidirect |
| 39. C2×Q16×C191 | C22 | semidirect |
| 41. #103×C191 | C22 | semidirect |
| 149. C191 | #3196 | semidirect |
| 159. #451 | D191 | semidirect |
| 165. C2×Q16 | C2×D191 | semidirect |
| 188. #103 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133176 | 2 |
| C2×#20259298 | 2 |
| #27133002 | 2 |
| #27132996 | 2 |
| #27132982 | 2 |
| #27132918 | 2 |
| #27132912 | 2 |
| #27132824 | 2 |
| #27132802 | 2 |
| #27132625 | 2 |
| #451×C191 | 2 |
| #3196 | 191 |