Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×C22⋊#11719910 | C2 | semidirect |
| 2. #20289636 | C2 | direct (N × H) |
| 6. C22⋊#11719910 | C22 | semidirect |
| 44. C23×D53 | C16 | semidirect |
| 101. C22×D53 | C2×C16 | semidirect |
| 160. C2×C53 | #1314 | semidirect |
| 175. C53 | C2×#1314 | semidirect |
| 319. C2 | #20289636 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11719910 | 2 |
| #20289636 | 2 |
| C22×#13133129 | 2 |
| C2×#1314 | 53 |