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 |
|---|---|---|
| 4. #27160986 | C2 | semidirect |
| 5. #27160985 | C2 | semidirect |
| 6. #27160984 | C2 | semidirect |
| 7. #27160983 | C2 | semidirect |
| 9. #391×C197 | C2 | semidirect |
| 14. C2×Q8×D197 | C4 | semidirect |
| 122. C197 | #2310 | semidirect |
| 131. #391 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D197 | 2 |
| C2×#20263284 | 2 |
| C2×#20263283 | 2 |
| #27160986 | 2 |
| #27160985 | 2 |
| #27160984 | 2 |
| #27160983 | 2 |
| #27160941 | 2 |
| #391×C197 | 2 |
| #2310 | 197 |