Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 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. #27133065 | C2 | semidirect |
| 3. #27133043 | C2 | semidirect |
| 4. #27133032 | C2 | semidirect |
| 7. #27132771 | C2 | semidirect |
| 8. C4×Dic764 | C2 | semidirect |
| 78. C191 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133275 | 2 |
| #27133065 | 2 |
| #27133043 | 2 |
| #27133032 | 2 |
| #27132921 | 2 |
| #27132904 | 2 |
| #27132771 | 2 |
| C4×Dic764 | 2 |
| #405×C191 | 2 |
| #3177 | 191 |