Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 27 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. #20272878 | C2 | semidirect |
| 2. #20272752 | C2 | semidirect |
| 6. D42×C53 | C4 | semidirect |
| 9. C53×#331 | C4 | semidirect |
| 92. D42 | Dic53 | semidirect |
| 97. #331 | Dic53 | semidirect |
| 99. C53 | #7515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272878 | 2 |
| #20272752 | 2 |
| C53×#1619 | 2 |
| #7515 | 53 |