Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1886 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 147 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×#16810347 | C2 | semidirect |
| 2. #20272643 | C2 | direct (N × H) |
| 6. #16810347 | C22 | semidirect |
| 24. C25×C53 | C8 | semidirect |
| 72. C24×C53 | C2×C8 | semidirect |
| 203. C2×C53 | #1316 | semidirect |
| 216. C53 | C2×#1316 | semidirect |
| 224. C25 | #88322 | semidirect |
| 273. C24 | C2×#88322 | semidirect |
| 402. C2 | #20272643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810347 | 2 |
| #20272643 | 2 |
| C2×C53×#379 | 2 |
| C2×#1316 | 53 |