Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 69. C197 | #1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161371 | 2 |
| #27161361 | 2 |
| C8×Dic394 | 2 |
| #27160832 | 2 |
| #27160828 | 2 |
| #27160825 | 2 |
| #487×C197 | 2 |
| #1684 | 197 |