Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #27163095 | C2 | semidirect |
| 2. #27163094 | C2 | semidirect |
| 3. #27163091 | C2 | semidirect |
| 4. #27163091 | C2 | semidirect |
| 5. #27163089 | C2 | semidirect |
| 6. #27163089 | C2 | semidirect |
| 7. #27163087 | C2 | semidirect |
| 8. #27163086 | C2 | semidirect |
| 12. #27163075 | C2 | semidirect |
| 13. #27163074 | C2 | semidirect |
| 14. #27163072 | C2 | semidirect |
| 15. C22⋊Q8×C397 | C2 | semidirect |
| 97. C397 | #563 | semidirect |
| 113. C22⋊Q8 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163095 | 2 |
| #27163094 | 2 |
| #27163091 | 2 |
| #27163089 | 2 |
| #27163087 | 2 |
| #27163086 | 2 |
| #27163082 | 2 |
| #27163079 | 2 |
| #27163078 | 2 |
| #27163075 | 2 |
| #27163074 | 2 |
| #27163072 | 2 |
| C22⋊Q8×C397 | 2 |
| #563 | 397 |