Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27163091 | C2 | semidirect |
| 2. #27163087 | C2 | semidirect |
| 3. #27163085 | C2 | semidirect |
| 4. #27163080 | C2 | semidirect |
| 6. Q8×Dic397 | C2 | semidirect |
| 7. #27163058 | C2 | semidirect |
| 8. #27163056 | C2 | semidirect |
| 9. #27163054 | C2 | semidirect |
| 10. C2×C4×Dic397 | C2 | semidirect |
| 11. C22⋊Q8×C397 | C2 | semidirect |
| 74. C397 | #529 | semidirect |
| 80. C22⋊Q8 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163091 | 2 |
| #27163087 | 2 |
| #27163085 | 2 |
| #27163080 | 2 |
| #27163070 | 2 |
| Q8×Dic397 | 2 |
| #27163058 | 2 |
| #27163056 | 2 |
| #27163054 | 2 |
| C2×C4×Dic397 | 2 |
| C22⋊Q8×C397 | 2 |
| #529 | 397 |