Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 132 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. #20290569 | C2 | semidirect |
| 2. #20289535 | C2 | semidirect |
| 3. #20289531 | C2 | semidirect |
| 37. C2×#41×C53 | C8 | semidirect |
| 180. C53 | #7597 | semidirect |
| 184. C2×#41 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290569 | 2 |
| #20289535 | 2 |
| #20289531 | 2 |
| #20277206 | 2 |
| #7597 | 53 |