Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
232 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #20263260 | C4 | semidirect |
| 10. #20263258 | C4 | semidirect |
| 13. C8×Dic197 | C4 | semidirect |
| 16. #108×C197 | C4 | semidirect |
| 64. C197 | #1772 | semidirect |
| 76. #108 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161117 | 2 |
| #27161037 | 2 |
| C2×C8×Dic197 | 2 |
| #27160840 | 2 |
| C2×#108×C197 | 2 |
| #1772 | 197 |