Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
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. #27189716 | C2 | semidirect |
| 2. #27189715 | C2 | semidirect |
| 3. #27189712 | C2 | semidirect |
| 4. #27189712 | C2 | semidirect |
| 5. #27189710 | C2 | semidirect |
| 6. #27189710 | C2 | semidirect |
| 7. #27189708 | C2 | semidirect |
| 8. #27189707 | C2 | semidirect |
| 12. #27189696 | C2 | semidirect |
| 13. #27189695 | C2 | semidirect |
| 14. #27189693 | C2 | semidirect |
| 15. C22⋊Q8×C409 | C2 | semidirect |
| 97. C409 | #563 | semidirect |
| 113. C22⋊Q8 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189716 | 2 |
| #27189715 | 2 |
| #27189712 | 2 |
| #27189710 | 2 |
| #27189708 | 2 |
| #27189707 | 2 |
| #27189703 | 2 |
| #27189700 | 2 |
| #27189699 | 2 |
| #27189696 | 2 |
| #27189695 | 2 |
| #27189693 | 2 |
| C22⋊Q8×C409 | 2 |
| #563 | 409 |