Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#20263249 | C2 | semidirect |
| 5. C2×#20263244 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #343×C197 | C2 | semidirect |
| 11. #20263359 | C4 | semidirect |
| 116. C197 | #1908 | semidirect |
| 123. #343 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263334 | 2 |
| #27161078 | 2 |
| C2×#20263249 | 2 |
| C2×#20263244 | 2 |
| #27160843 | 2 |
| #343×C197 | 2 |
| #1908 | 197 |