Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
224 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 12. #20263261 | C4 | semidirect |
| 13. #20263259 | C4 | semidirect |
| 14. #20263257 | C4 | semidirect |
| 16. #20263237 | C4 | semidirect |
| 79. C197 | #1773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263261 | 2 |
| #27161115 | 2 |
| #27161037 | 2 |
| #27161035 | 2 |
| C2×#20263237 | 2 |
| #27160839 | 2 |
| #339×C197 | 2 |
| #1773 | 197 |