Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1116 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20290570 | C2 | semidirect |
| 2. C4×#13133274 | C2 | semidirect |
| 3. C2×D4⋊#88324 | C2 | semidirect |
| 226. C53 | #8313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290570 | 2 |
| C4×#13133274 | 2 |
| C2×D4⋊#88324 | 2 |
| C2×#16811171 | 2 |
| #8313 | 53 |