Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
274 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 7. #16811545 | C4 | semidirect |
| 9. C8×#88324 | C4 | semidirect |
| 24. #13133151 | C8 | semidirect |
| 35. #108×C53 | C8 | semidirect |
| 113. C53 | #7179 | semidirect |
| 124. #108 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811545 | 2 |
| C2×C8×#88324 | 2 |
| #20274597 | 2 |
| #7179 | 53 |