Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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. #27133140 | C2 | semidirect |
| 3. #27132637 | C2 | semidirect |
| 4. #27132636 | C2 | semidirect |
| 5. #27132635 | C2 | semidirect |
| 6. #410×C191 | C2 | semidirect |
| 9. C2×#15690287 | C4 | semidirect |
| 11. C2×#15690286 | C4 | semidirect |
| 13. C22×Dic382 | C4 | semidirect |
| 15. C2×Q8×D191 | C4 | semidirect |
| 113. C191 | #2884 | semidirect |
| 120. #410 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259369 | 2 |
| #27133140 | 2 |
| #27132637 | 2 |
| #27132636 | 2 |
| #27132635 | 2 |
| #410×C191 | 2 |
| #2884 | 191 |