Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #27132949 | C2 | semidirect |
| 4. #27132948 | C2 | semidirect |
| 5. #27132946 | C2 | semidirect |
| 8. #27132871 | C2 | semidirect |
| 9. #27132870 | C2 | semidirect |
| 11. #462×C191 | C2 | semidirect |
| 129. C191 | #3255 | semidirect |
| 140. #462 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133217 | 2 |
| #27132949 | 2 |
| #27132948 | 2 |
| #27132946 | 2 |
| #27132920 | 2 |
| #27132918 | 2 |
| #27132871 | 2 |
| #27132870 | 2 |
| #27132685 | 2 |
| #462×C191 | 2 |
| #3255 | 191 |