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. #27160983 | C2 | semidirect |
| 3. #27160973 | C2 | semidirect |
| 4. #27160967 | C2 | semidirect |
| 6. C22⋊C4×Dic197 | C2 | semidirect |
| 7. C4×C22⋊Dic197 | C2 | semidirect |
| 8. #27160924 | C2 | semidirect |
| 12. #20263313 | C4 | semidirect |
| 34. C2×Dic394 | C2×C4 | semidirect |
| 44. C22⋊Dic197 | C2×C4 | semidirect |
| 45. C22⋊Dic197 | C2×C4 | semidirect |
| 49. C4×Dic197 | C2×C4 | semidirect |
| 127. C197 | #2372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263313 | 2 |
| #27160983 | 2 |
| #27160973 | 2 |
| #27160967 | 2 |
| #27160959 | 2 |
| C22⋊C4×Dic197 | 2 |
| C4×C22⋊Dic197 | 2 |
| #27160924 | 2 |
| #386×C197 | 2 |
| #2372 | 197 |