Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20290952 | C2 | semidirect |
| 2. #20290597 | C2 | semidirect |
| 3. #20289688 | C2 | semidirect |
| 4. #20289686 | C2 | semidirect |
| 12. C2×#13133239 | C4 | semidirect |
| 15. #16810882 | C4 | semidirect |
| 17. #16810877 | C4 | semidirect |
| 22. C2×#106×C53 | C4 | semidirect |
| 188. C2×#106 | #6157 | semidirect |
| 194. C53 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290952 | 2 |
| #20290597 | 2 |
| #20289688 | 2 |
| #20289686 | 2 |
| #20284378 | 2 |
| #11867 | 53 |