Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 136 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. C22×#13133267 | C2 | semidirect |
| 2. #20289829 | C2 | direct (N × H) |
| 5. C2×#13133267 | C22 | semidirect |
| 49. C22×D53 | C32 | semidirect |
| 72. C2×D53 | C2×C32 | semidirect |
| 80. C2×C53 | C22⋊C32 | semidirect |
| 93. C53 | C2×C22⋊C32 | semidirect |
| 159. C2 | #20289829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133267 | 2 |
| #20289829 | 2 |
| C22×C16×D53 | 2 |
| C2×C22⋊C32 | 53 |