Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161808 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161425 | C2 | semidirect |
| 5. #27161377 | C2 | semidirect |
| 6. #27161360 | C2 | semidirect |
| 7. #27161277 | C2 | semidirect |
| 8. #27161206 | C2 | semidirect |
| 9. #27161180 | C2 | semidirect |
| 10. C4×#15691345 | C2 | semidirect |
| 11. #460×C197 | C2 | semidirect |
| 91. Q8×C197 | #41 | semidirect |
| 124. C197 | #3368 | semidirect |
| 133. #460 | D197 | semidirect |
| 204. Q8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161808 | 2 |
| #27161749 | 2 |
| #27161442 | 2 |
| #27161425 | 2 |
| #27161377 | 2 |
| #27161360 | 2 |
| #27161277 | 2 |
| #27161206 | 2 |
| #27161180 | 2 |
| C4×#15691345 | 2 |
| #460×C197 | 2 |
| #3368 | 197 |