Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#16810421 | C2 | semidirect |
| 4. #20274711 | C2 | semidirect |
| 5. C4×#101×C53 | C2 | semidirect |
| 187. C4×#101 | D53 | semidirect |
| 213. C53 | #13228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279691 | 2 |
| C2×#16810421 | 2 |
| C2×#16810419 | 2 |
| #20274711 | 2 |
| C4×#101×C53 | 2 |
| #13228 | 53 |