Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #27160983 | C2 | semidirect |
| 3. #27160974 | C2 | semidirect |
| 6. #27160962 | C2 | semidirect |
| 7. #27160960 | C2 | semidirect |
| 11. #20263305 | C4 | semidirect |
| 110. C197 | #2378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263305 | 2 |
| #27160983 | 2 |
| #27160974 | 2 |
| #27160973 | 2 |
| #27160967 | 2 |
| #27160962 | 2 |
| #27160960 | 2 |
| #27160942 | 2 |
| #380×C197 | 2 |
| #2378 | 197 |