Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #27133060 | C2 | semidirect |
| 3. #27133041 | C2 | semidirect |
| 4. #27133012 | C2 | semidirect |
| 7. #27132770 | C2 | semidirect |
| 8. #27132769 | C2 | semidirect |
| 9. #27132767 | C2 | semidirect |
| 105. C191 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133215 | 2 |
| #27133060 | 2 |
| #27133041 | 2 |
| #27133012 | 2 |
| #27132921 | 2 |
| #27132919 | 2 |
| #27132770 | 2 |
| #27132769 | 2 |
| #27132767 | 2 |
| M16×Dic191 | 2 |
| #470×C191 | 2 |
| #3185 | 191 |