Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×D788 | C2 | semidirect |
| 2. #27161426 | C2 | semidirect |
| 3. #27161279 | C2 | semidirect |
| 5. #27160824 | C2 | semidirect |
| 6. #27160808 | C2 | semidirect |
| 7. Q8⋊C8×C197 | C2 | semidirect |
| 62. D788 | SD16 | semidirect |
| 70. Q8×C197 | D8 | semidirect |
| 99. C197 | #1627 | semidirect |
| 106. Q8⋊C8 | D197 | semidirect |
| 157. Q8 | D1576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D788 | 2 |
| #27161426 | 2 |
| #27161279 | 2 |
| #27161275 | 2 |
| #27160824 | 2 |
| #27160808 | 2 |
| Q8⋊C8×C197 | 2 |
| #1627 | 197 |