Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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. #27160971 | C2 | semidirect |
| 4. #27160968 | C2 | semidirect |
| 6. #27160953 | C2 | semidirect |
| 7. C4×C4⋊Dic197 | C2 | semidirect |
| 8. #27160926 | C2 | semidirect |
| 9. #383×C197 | C2 | semidirect |
| 13. #20263314 | C4 | semidirect |
| 34. C2×Dic394 | C2×C4 | semidirect |
| 48. #15691335 | C2×C4 | semidirect |
| 49. #15691335 | C2×C4 | semidirect |
| 58. C42×C197 | C2×C4 | semidirect |
| 118. C197 | #2337 | semidirect |
| 126. #383 | D197 | semidirect |
| 177. C42 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263314 | 2 |
| #27160983 | 2 |
| #27160971 | 2 |
| #27160968 | 2 |
| #27160957 | 2 |
| #27160953 | 2 |
| C4×C4⋊Dic197 | 2 |
| #27160926 | 2 |
| #383×C197 | 2 |
| #2337 | 197 |