Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #27161710 | C2 | semidirect |
| 3. #27161388 | C2 | semidirect |
| 4. #27161377 | C2 | semidirect |
| 5. #27161367 | C2 | semidirect |
| 6. #27161362 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. C2×#20263257 | C2 | semidirect |
| 9. #27161107 | C2 | semidirect |
| 64. #41×C197 | Q8 | semidirect |
| 123. C197 | #3084 | semidirect |
| 166. #41 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161710 | 2 |
| #27161562 | 2 |
| #27161388 | 2 |
| #27161377 | 2 |
| #27161367 | 2 |
| #27161362 | 2 |
| #27161121 | 2 |
| C2×#20263257 | 2 |
| #27161107 | 2 |
| #27161075 | 2 |
| #417×C197 | 2 |
| #3084 | 197 |