Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 1. #27161127 | C2 | semidirect |
| 2. #27161102 | C2 | semidirect |
| 5. #27160850 | C2 | semidirect |
| 6. #27160840 | C2 | semidirect |
| 15. #20263253 | C4 | semidirect |
| 16. #20263253 | C4 | semidirect |
| 97. C197 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161127 | 2 |
| #27161102 | 2 |
| #27161096 | 2 |
| C2×#20263253 | 2 |
| #27160850 | 2 |
| #27160840 | 2 |
| #568×C197 | 2 |
| #1861 | 197 |