Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic191 | C2 | semidirect |
| 3. #27132996 | C2 | semidirect |
| 5. #27132968 | C2 | semidirect |
| 6. #27132887 | C2 | semidirect |
| 8. #27132770 | C2 | semidirect |
| 9. #27132766 | C2 | semidirect |
| 10. #27132717 | C2 | semidirect |
| 11. #451×C191 | C2 | semidirect |
| 131. C191 | #3117 | semidirect |
| 139. #451 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133199 | 2 |
| C2×Q8×Dic191 | 2 |
| #27132996 | 2 |
| #27132982 | 2 |
| #27132968 | 2 |
| #27132887 | 2 |
| #27132802 | 2 |
| #27132770 | 2 |
| #27132766 | 2 |
| #27132717 | 2 |
| #451×C191 | 2 |
| #3117 | 191 |