Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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. #27132742 | C2 | semidirect |
| 3. #27132733 | C2 | semidirect |
| 4. C8×D764 | C2 | semidirect |
| 5. #27132720 | C2 | semidirect |
| 6. #27132628 | C2 | semidirect |
| 7. #431×C191 | C2 | semidirect |
| 92. C191 | #2981 | semidirect |
| 99. #431 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| #27132742 | 2 |
| #27132733 | 2 |
| C8×D764 | 2 |
| #27132720 | 2 |
| #27132628 | 2 |
| #431×C191 | 2 |
| #2981 | 191 |