Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20263356 | C2 | semidirect |
| 3. #27161846 | C2 | semidirect |
| 4. #27161352 | C2 | semidirect |
| 5. #27161340 | C2 | semidirect |
| 6. #27161127 | C2 | semidirect |
| 7. #27161063 | C2 | semidirect |
| 8. C2×#20263244 | C2 | semidirect |
| 16. C2×#15691348 | C22 | semidirect |
| 18. C2×#15691346 | C22 | semidirect |
| 25. #20263261 | C22 | semidirect |
| 26. #20263245 | C22 | semidirect |
| 27. #20263244 | C22 | semidirect |
| 28. #20263243 | C22 | semidirect |
| 142. C197 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| #27161846 | 2 |
| #27161352 | 2 |
| #27161340 | 2 |
| #27161127 | 2 |
| #27161063 | 2 |
| C2×#20263244 | 2 |
| #575×C197 | 2 |
| #3069 | 197 |