Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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×#20263272 | C2 | semidirect |
| 4. #27160906 | C2 | semidirect |
| 5. #27160883 | C2 | semidirect |
| 6. #27160882 | C2 | semidirect |
| 71. C197 | #2219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263272 | 2 |
| C2×#20263266 | 2 |
| #27161320 | 2 |
| #27160906 | 2 |
| #27160883 | 2 |
| #27160882 | 2 |
| #467×C197 | 2 |
| #2219 | 197 |