Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 256 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. #27161734 | C2 | semidirect |
| 2. #27161425 | C2 | semidirect |
| 3. #27161271 | C2 | semidirect |
| 4. #27160824 | C2 | semidirect |
| 5. D4⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #459×C197 | C2 | semidirect |
| 55. D788 | D8 | semidirect |
| 104. C197 | #1625 | semidirect |
| 109. #459 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161734 | 2 |
| #27161425 | 2 |
| #27161271 | 2 |
| #27160824 | 2 |
| D4⋊#13096802 | 2 |
| #27160806 | 2 |
| #459×C197 | 2 |
| #1625 | 197 |