Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#20263356 | C2 | semidirect |
| 2. C2×#20263305 | C2 | semidirect |
| 3. #27161241 | C2 | semidirect |
| 4. #27161235 | C2 | semidirect |
| 5. #27161230 | C2 | semidirect |
| 6. #27161080 | C2 | semidirect |
| 7. #27161043 | C2 | semidirect |
| 9. C22×Dic394 | C22 | semidirect |
| 11. C2×#15691348 | C22 | semidirect |
| 12. C2×#15691346 | C22 | semidirect |
| 13. C2×#15691342 | C22 | semidirect |
| 17. #20263305 | C22 | semidirect |
| 18. C2×C4⋊Dic197 | C22 | semidirect |
| 21. #20263250 | C22 | semidirect |
| 22. #20263247 | C22 | semidirect |
| 24. C22⋊#13096802 | C22 | semidirect |
| 130. C22×C197 | #137 | semidirect |
| 146. C197 | #3007 | semidirect |
| 277. C22 | #20263356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C2×#20263305 | 2 |
| #27161241 | 2 |
| #27161235 | 2 |
| #27161230 | 2 |
| #27161080 | 2 |
| #27161043 | 2 |
| C22×#41×C197 | 2 |
| #3007 | 197 |