Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27161552 | C2 | semidirect |
| 3. C2×#20263240 | C2 | semidirect |
| 4. #27160934 | C2 | semidirect |
| 5. #27160934 | C2 | semidirect |
| 6. #27160845 | C2 | semidirect |
| 7. #342×C197 | C2 | semidirect |
| 12. #20263296 | C4 | semidirect |
| 33. C23×D197 | C2×C4 | semidirect |
| 45. C22×Dic197 | D4 | semidirect |
| 60. C22×C4×C197 | D4 | semidirect |
| 66. C22⋊C4×C197 | C2×C4 | semidirect |
| 87. C22×D197 | C22⋊C4 | semidirect |
| 99. C2×Dic197 | C22⋊C4 | semidirect |
| 160. C197 | #1889 | semidirect |
| 168. #342 | D197 | semidirect |
| 211. C22×C4 | D788 | semidirect |
| 226. C22⋊C4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263296 | 2 |
| #27161552 | 2 |
| C2×#20263240 | 2 |
| #27160934 | 2 |
| #27160845 | 2 |
| #342×C197 | 2 |
| #1889 | 197 |