Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27160959 | C2 | semidirect |
| 3. #27160958 | C2 | semidirect |
| 4. #27160957 | C2 | semidirect |
| 5. #27160956 | C2 | semidirect |
| 6. #27160955 | C2 | semidirect |
| 7. #27160955 | C2 | semidirect |
| 8. #27160946 | C2 | semidirect |
| 9. #386×C197 | C2 | semidirect |
| 15. #20263322 | C4 | semidirect |
| 35. C2×D788 | C2×C4 | semidirect |
| 40. C2×C22⋊D197 | C2×C4 | semidirect |
| 41. C2×C22⋊D197 | C2×C4 | semidirect |
| 55. C4×Dic197 | C2×C4 | semidirect |
| 60. C2×D4×C197 | C2×C4 | semidirect |
| 147. C197 | #2380 | semidirect |
| 156. #386 | D197 | semidirect |
| 194. C2×D4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263322 | 2 |
| #27160959 | 2 |
| #27160958 | 2 |
| #27160957 | 2 |
| #27160956 | 2 |
| #27160955 | 2 |
| #27160946 | 2 |
| #386×C197 | 2 |
| #2380 | 197 |