Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161802 | C2 | semidirect |
| 2. #27161425 | C2 | semidirect |
| 4. #27160824 | C2 | semidirect |
| 5. Q8⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #460×C197 | C2 | semidirect |
| 95. C197 | #1628 | semidirect |
| 99. #460 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| #27161425 | 2 |
| #27161271 | 2 |
| #27160824 | 2 |
| Q8⋊#13096802 | 2 |
| #27160806 | 2 |
| #460×C197 | 2 |
| #1628 | 197 |