Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1318 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 91. C2×C4×C53 | #101 | semidirect |
| 99. C2×Dic53 | #101 | semidirect |
| 144. C53 | #10983 | semidirect |
| 238. C2×C4 | #13133278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133278 | 2 |
| #20290378 | 2 |
| C22×#13133216 | 2 |
| #10983 | 53 |