Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C23×#11719917 | C2 | semidirect |
| 2. C22×#13133134 | C2 | direct (N × H) |
| 5. C22×#11719917 | C22 | semidirect |
| 7. C2×#13133134 | C22 | direct (N × H) |
| 15. C2×#11719917 | C23 | semidirect |
| 17. #13133134 | C23 | direct (N × H) |
| 56. #11719917 | C24 | semidirect |
| 65. C23×C53 | #100 | semidirect |
| 86. C22×C53 | C2×#100 | semidirect |
| 98. C2×C53 | C22×#100 | semidirect |
| 110. C53 | C23×#100 | semidirect |
| 162. C23 | #13133134 | direct (N × H) |
| 182. C22 | C2×#13133134 | direct (N × H) |
| 191. C2 | C22×#13133134 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719917 | 2 |
| C22×#13133134 | 2 |
| C24×D4×C53 | 2 |
| C23×#100 | 53 |