Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27133064 | C2 | semidirect |
| 3. #27133041 | C2 | semidirect |
| 4. #27133030 | C2 | semidirect |
| 8. #27132768 | C2 | semidirect |
| 9. C4×Dic764 | C2 | semidirect |
| 11. C4×Q16×C191 | C2 | semidirect |
| 111. C191 | #3177 | semidirect |
| 122. C4×Q16 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133271 | 2 |
| #27133064 | 2 |
| #27133041 | 2 |
| #27133030 | 2 |
| #27132920 | 2 |
| #27132905 | 2 |
| #27132901 | 2 |
| #27132768 | 2 |
| C4×Dic764 | 2 |
| #27132617 | 2 |
| C4×Q16×C191 | 2 |
| #3177 | 191 |