Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 11. #16811464 | C4 | semidirect |
| 12. C8×#88324 | C4 | semidirect |
| 15. #16810345 | C4 | semidirect |
| 16. C8×#88322 | C4 | semidirect |
| 17. C82×C53 | C4 | semidirect |
| 25. C8×#6157 | C8 | semidirect |
| 105. C82 | #6157 | semidirect |
| 106. C53 | #8137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290371 | 2 |
| #20289919 | 2 |
| #20289540 | 2 |
| #20289538 | 2 |
| #20272997 | 2 |
| #8137 | 53 |