Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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. C4⋊#15691333 | C2 | semidirect |
| 5. #27160882 | C2 | semidirect |
| 7. C4×Q16×C197 | C2 | semidirect |
| 72. C197 | #2211 | semidirect |
| 77. C4×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263272 | 2 |
| C2×#20263269 | 2 |
| #27161463 | 2 |
| C4⋊#15691333 | 2 |
| #27160882 | 2 |
| #27160879 | 2 |
| C4×Q16×C197 | 2 |
| #2211 | 197 |