Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 8. #20263237 | C4 | semidirect |
| 9. #20263236 | C4 | semidirect |
| 10. C8×Dic197 | C4 | semidirect |
| 15. C4×C8×C197 | C4 | semidirect |
| 53. C197 | #1726 | semidirect |
| 68. C4×C8 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263237 | 2 |
| C2×#20263236 | 2 |
| C2×C8×Dic197 | 2 |
| #27160925 | 2 |
| C2×C4×C8×C197 | 2 |
| #1726 | 197 |