Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #20274711 | C2 | semidirect |
| 2. #20273473 | C2 | semidirect |
| 5. C2×Q8⋊#88322 | C2 | semidirect |
| 6. #20272589 | C2 | semidirect |
| 217. C53 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274711 | 2 |
| #20273473 | 2 |
| #20273392 | 2 |
| #20273166 | 2 |
| C2×Q8⋊#88322 | 2 |
| #20272589 | 2 |
| C53×#3037 | 2 |
| #10458 | 53 |