Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #27160974 | C2 | semidirect |
| 4. #27160960 | C2 | semidirect |
| 6. #27160947 | C2 | semidirect |
| 7. #384×C197 | C2 | semidirect |
| 9. #20263320 | C4 | semidirect |
| 28. #15691337 | C2×C4 | semidirect |
| 37. C42×C197 | C2×C4 | semidirect |
| 72. C197 | #2383 | semidirect |
| 79. #384 | D197 | semidirect |
| 110. C42 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263320 | 2 |
| #27160974 | 2 |
| #27160969 | 2 |
| #27160960 | 2 |
| #27160950 | 2 |
| #27160947 | 2 |
| #384×C197 | 2 |
| #2383 | 197 |