Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #27161611 | C2 | semidirect |
| 2. #27161480 | C2 | semidirect |
| 3. #27161462 | C2 | semidirect |
| 4. #27161432 | C2 | semidirect |
| 5. #27161321 | C2 | semidirect |
| 7. #27161307 | C2 | semidirect |
| 8. C4×Dic788 | C2 | semidirect |
| 9. C4×#15691346 | C2 | semidirect |
| 10. C4×C8×D197 | C2 | semidirect |
| 11. C4×D8×C197 | C2 | semidirect |
| 118. C197 | #3168 | semidirect |
| 129. C4×D8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161611 | 2 |
| #27161480 | 2 |
| #27161462 | 2 |
| #27161432 | 2 |
| #27161321 | 2 |
| #27161312 | 2 |
| #27161307 | 2 |
| C4×Dic788 | 2 |
| C4×#15691346 | 2 |
| C4×C8×D197 | 2 |
| C4×D8×C197 | 2 |
| #3168 | 197 |