Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20259280 | C2 | semidirect |
| 3. #27133003 | C2 | semidirect |
| 4. #27133002 | C2 | semidirect |
| 5. #27132986 | C2 | semidirect |
| 6. #27132985 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. #27132703 | C2 | semidirect |
| 9. #27132664 | C2 | semidirect |
| 10. #27132626 | C2 | semidirect |
| 11. #417×C191 | C2 | semidirect |
| 30. #20259256 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. #20259254 | C22 | semidirect |
| 33. #20259253 | C22 | semidirect |
| 34. #20259246 | C22 | semidirect |
| 35. #20259243 | C22 | semidirect |
| 41. #103×C191 | C22 | semidirect |
| 42. #102×C191 | C22 | semidirect |
| 152. C191 | #3093 | semidirect |
| 163. #417 | D191 | semidirect |
| 191. #103 | C2×D191 | semidirect |
| 193. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133170 | 2 |
| C2×#20259280 | 2 |
| #27133003 | 2 |
| #27133002 | 2 |
| #27132986 | 2 |
| #27132985 | 2 |
| #27132705 | 2 |
| #27132703 | 2 |
| #27132664 | 2 |
| #27132626 | 2 |
| #417×C191 | 2 |
| #3093 | 191 |