Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27160979 | C2 | semidirect |
| 3. #27160969 | C2 | semidirect |
| 4. #27160964 | C2 | semidirect |
| 5. #27160957 | C2 | semidirect |
| 6. #27160955 | C2 | semidirect |
| 7. #27160950 | C2 | semidirect |
| 8. #27160942 | C2 | semidirect |
| 9. #380×C197 | C2 | semidirect |
| 13. #20263300 | C4 | semidirect |
| 37. C2×C22⋊D197 | C2×C4 | semidirect |
| 44. C4⋊Dic197 | C2×C4 | semidirect |
| 50. #15691335 | C2×C4 | semidirect |
| 54. C22×C4×C197 | C2×C4 | semidirect |
| 129. C197 | #2377 | semidirect |
| 139. #380 | D197 | semidirect |
| 176. C22×C4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263300 | 2 |
| #27160979 | 2 |
| #27160969 | 2 |
| #27160964 | 2 |
| #27160957 | 2 |
| #27160955 | 2 |
| #27160950 | 2 |
| #27160942 | 2 |
| #380×C197 | 2 |
| #2377 | 197 |