Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161562 | C2 | semidirect |
| 2. #27161417 | C2 | semidirect |
| 3. #27161412 | C2 | semidirect |
| 4. #27161400 | C2 | semidirect |
| 5. #27161390 | C2 | semidirect |
| 6. #27161119 | C2 | semidirect |
| 7. C2×#20263259 | C2 | semidirect |
| 8. #27161080 | C2 | semidirect |
| 9. #27161075 | C2 | semidirect |
| 10. #27161046 | C2 | semidirect |
| 133. C197 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161562 | 2 |
| #27161417 | 2 |
| #27161412 | 2 |
| #27161400 | 2 |
| #27161390 | 2 |
| #27161119 | 2 |
| C2×#20263259 | 2 |
| #27161080 | 2 |
| #27161075 | 2 |
| #27161046 | 2 |
| #537×C197 | 2 |
| #3098 | 197 |