Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#20263257 | C2 | semidirect |
| 5. #27160841 | C2 | semidirect |
| 6. #27160834 | C2 | semidirect |
| 7. #389×C197 | C2 | semidirect |
| 18. #20263246 | C4 | semidirect |
| 40. C2×#13096802 | C2×C4 | semidirect |
| 53. C4⋊C4×C197 | C2×C4 | semidirect |
| 66. D788 | C4⋊C4 | semidirect |
| 123. C197 | #1864 | semidirect |
| 129. #389 | D197 | semidirect |
| 176. C4⋊C4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D788 | 2 |
| C2×#20263257 | 2 |
| C2×#20263246 | 2 |
| #27160841 | 2 |
| #27160834 | 2 |
| #389×C197 | 2 |
| #1864 | 197 |