Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20291516 | C2 | semidirect |
| 4. #20290045 | C2 | semidirect |
| 5. #20289585 | C2 | semidirect |
| 6. #20289560 | C2 | semidirect |
| 121. #11719940 | SD16 | semidirect |
| 196. Dic106 | #100 | semidirect |
| 272. C53 | #9254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291516 | 2 |
| #20290857 | 2 |
| #20290222 | 2 |
| #20290045 | 2 |
| #20289585 | 2 |
| #20289560 | 2 |
| C2×#16810822 | 2 |
| #9254 | 53 |