Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1058 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 2. #20289553 | C2 | semidirect |
| 6. #16811593 | C4 | semidirect |
| 53. C22×C4×C53 | M16 | semidirect |
| 73. C22×Dic53 | M16 | semidirect |
| 186. C53 | #7911 | semidirect |
| 248. C22×C4 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811593 | 2 |
| #20289553 | 2 |
| C2×C22⋊C4×Dic53 | 2 |
| #7911 | 53 |