Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 1. #27132741 | C2 | semidirect |
| 2. #27132735 | C2 | semidirect |
| 3. #27132724 | C2 | semidirect |
| 4. #27132630 | C2 | semidirect |
| 5. #27132627 | C2 | semidirect |
| 8. C2×#15690271 | C22 | semidirect |
| 9. C22×C191⋊C8 | C22 | semidirect |
| 10. C4⋊(C191⋊C8) | C22 | semidirect |
| 14. C22⋊(C191⋊C8) | C22 | semidirect |
| 15. #20259233 | C22 | semidirect |
| 16. C4×C191⋊C8 | C22 | semidirect |
| 89. C191 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132741 | 2 |
| #27132735 | 2 |
| #27132724 | 2 |
| #27132630 | 2 |
| #27132627 | 2 |
| #525×C191 | 2 |
| #2978 | 191 |