Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
|---|---|---|
| 5. C4×#11719910 | C4 | semidirect |
| 31. C42×C53 | C16 | semidirect |
| 82. C53 | #12590 | semidirect |
| 110. C42 | #11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719910 | 2 |
| #20289753 | 2 |
| C42×#88322 | 2 |
| #12590 | 53 |