Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 105. Q8×C53 | #108 | semidirect |
| 127. Dic106 | #108 | semidirect |
| 184. C53 | #8659 | semidirect |
| 268. Q8 | #13133288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290656 | 2 |
| #20290265 | 2 |
| #20290044 | 2 |
| #20289607 | 2 |
| C8×Q8×D53 | 2 |
| #8659 | 53 |