Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #27160983 | C2 | semidirect |
| 8. C22×Dic394 | C4 | semidirect |
| 75. C197 | #2310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic394 | 2 |
| C2×#20263282 | 2 |
| #27160983 | 2 |
| #27160942 | 2 |
| #27160940 | 2 |
| #381×C197 | 2 |
| #2310 | 197 |