Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20263349 | C2 | semidirect |
| 2. #27161751 | C2 | semidirect |
| 3. #27161456 | C2 | semidirect |
| 4. #27161316 | C2 | semidirect |
| 5. #27161279 | C2 | semidirect |
| 6. #27161227 | C2 | semidirect |
| 7. C8×D788 | C2 | semidirect |
| 8. C4×Q16×C197 | C2 | semidirect |
| 48. Q16×C197 | D4 | semidirect |
| 88. C4×C197 | #135 | semidirect |
| 97. C197 | #3287 | semidirect |
| 105. C4×Q16 | D197 | semidirect |
| 138. Q16 | D788 | semidirect |
| 187. C4 | #20263349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| #27161751 | 2 |
| #27161456 | 2 |
| #27161316 | 2 |
| #27161279 | 2 |
| #27161227 | 2 |
| C8×D788 | 2 |
| C4×Q16×C197 | 2 |
| #3287 | 197 |