Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27161789 | C2 | semidirect |
| 2. #27161452 | C2 | semidirect |
| 3. #27161279 | C2 | semidirect |
| 5. #27160827 | C2 | semidirect |
| 6. #27160808 | C2 | semidirect |
| 7. Q8⋊C8×C197 | C2 | semidirect |
| 59. D788 | SD16 | semidirect |
| 96. C197 | #1622 | semidirect |
| 103. Q8⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161789 | 2 |
| #27161452 | 2 |
| #27161279 | 2 |
| #27161275 | 2 |
| #27160827 | 2 |
| #27160808 | 2 |
| Q8⋊C8×C197 | 2 |
| #1622 | 197 |