Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 12. #20263888 | C4 | semidirect |
| 13. #20263888 | C4 | semidirect |
| 14. #20263886 | C4 | semidirect |
| 15. #20263886 | C4 | semidirect |
| 88. C199 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164054 | 2 |
| #27163973 | 2 |
| #27163782 | 2 |
| #27163779 | 2 |
| #27163777 | 2 |
| #27163772 | 2 |
| #424×C199 | 2 |
| #1922 | 199 |