Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #27160986 | C2 | semidirect |
| 3. #27160971 | C2 | semidirect |
| 4. #27160969 | C2 | semidirect |
| 6. C4×#15691335 | C2 | semidirect |
| 7. #27160926 | C2 | semidirect |
| 8. #27160924 | C2 | semidirect |
| 9. #391×C197 | C2 | semidirect |
| 12. #20263315 | C4 | semidirect |
| 46. #15691335 | C2×C4 | semidirect |
| 47. #15691335 | C2×C4 | semidirect |
| 51. C4×Dic197 | C2×C4 | semidirect |
| 54. C2×Q8×C197 | C2×C4 | semidirect |
| 123. C197 | #2372 | semidirect |
| 127. #391 | D197 | semidirect |
| 159. C2×Q8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263315 | 2 |
| #27160986 | 2 |
| #27160971 | 2 |
| #27160969 | 2 |
| #27160957 | 2 |
| C4×#15691335 | 2 |
| #27160926 | 2 |
| #27160924 | 2 |
| #391×C197 | 2 |
| #2372 | 197 |