Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15691346 | C2 | semidirect |
| 3. #27161556 | C2 | semidirect |
| 4. #27161298 | C2 | semidirect |
| 5. #27161276 | C2 | semidirect |
| 6. #27161106 | C2 | semidirect |
| 7. #27161084 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 12. C2×#15691348 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 18. C4×Dic394 | C22 | semidirect |
| 22. C4⋊#13096802 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 35. C2×Dic394 | D4 | semidirect |
| 116. C197 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C22×#15691346 | 2 |
| #27161556 | 2 |
| #27161298 | 2 |
| #27161276 | 2 |
| #27161106 | 2 |
| #27161084 | 2 |
| #27161075 | 2 |
| #535×C197 | 2 |
| #3043 | 197 |