Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1246 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 308 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. C22×#88324 | Q8 | semidirect |
| 21. C22×Q8×C53 | C8 | semidirect |
| 87. C53 | #11380 | semidirect |
| 90. C22×Q8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811489 | 2 |
| C22×Q8×Dic53 | 2 |
| #11380 | 53 |