Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #20272917 | C2 | semidirect |
| 3. #20272915 | C2 | semidirect |
| 9. C2×C32×C53 | C4 | semidirect |
| 59. C2×C32 | Dic53 | semidirect |
| 64. C53 | #13633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276499 | 2 |
| #20272917 | 2 |
| #20272915 | 2 |
| C22×C32×C53 | 2 |
| #13633 | 53 |