Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#20263269 | C2 | semidirect |
| 2. C2×#20263267 | C2 | semidirect |
| 3. #27161315 | C2 | semidirect |
| 4. #27160883 | C2 | semidirect |
| 5. #27160880 | C2 | semidirect |
| 6. C22⋊#15691333 | C2 | semidirect |
| 7. C2×#135×C197 | C2 | semidirect |
| 39. Q16×C197 | D4 | semidirect |
| 42. D8×C197 | D4 | semidirect |
| 89. C197 | #2186 | semidirect |
| 91. C2×#135 | D197 | semidirect |
| 123. Q16 | C22⋊D197 | semidirect |
| 128. D8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263269 | 2 |
| C2×#20263267 | 2 |
| #27161315 | 2 |
| #27160883 | 2 |
| #27160880 | 2 |
| C22⋊#15691333 | 2 |
| C2×#135×C197 | 2 |
| #2186 | 197 |