Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 13. #16811001 | C4 | semidirect |
| 186. C53 | #13262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811001 | 2 |
| C2×#16810443 | 2 |
| C2×#16810440 | 2 |
| C2×#16810439 | 2 |
| #20276434 | 2 |
| #20274596 | 2 |
| C53×#2141 | 2 |
| #13262 | 53 |