Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27132672 | C2 | semidirect |
| 5. #27132433 | C2 | semidirect |
| 6. #27132419 | C2 | semidirect |
| 7. #519×C191 | C2 | semidirect |
| 11. C2×#15690277 | C4 | semidirect |
| 12. C2×#15690274 | C4 | semidirect |
| 109. C191 | #1905 | semidirect |
| 112. #519 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| #27132681 | 2 |
| #27132672 | 2 |
| #27132636 | 2 |
| #27132433 | 2 |
| #27132419 | 2 |
| #519×C191 | 2 |
| #1905 | 191 |