Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#20263358 | C2 | semidirect |
| 2. C2×#20263355 | C2 | semidirect |
| 4. C4⋊Q8×D197 | C2 | semidirect |
| 5. #27161474 | C2 | semidirect |
| 6. #27161473 | C2 | semidirect |
| 7. #27161471 | C2 | semidirect |
| 8. #27161457 | C2 | semidirect |
| 9. #27161450 | C2 | semidirect |
| 10. #27161031 | C2 | semidirect |
| 11. #497×C197 | C2 | semidirect |
| 63. #15691341 | D4 | semidirect |
| 124. Dic197 | #137 | semidirect |
| 130. C197 | #3152 | semidirect |
| 139. #497 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263358 | 2 |
| C2×#20263355 | 2 |
| #27161628 | 2 |
| C4⋊Q8×D197 | 2 |
| #27161474 | 2 |
| #27161473 | 2 |
| #27161471 | 2 |
| #27161457 | 2 |
| #27161450 | 2 |
| #27161031 | 2 |
| #497×C197 | 2 |
| #3152 | 197 |