Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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×D1696 | C2 | semidirect |
| 2. #20276801 | C2 | semidirect |
| 3. #20272915 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. C22×C32×C53 | C2 | semidirect |
| 27. C32×C53 | D4 | semidirect |
| 58. C22×C53 | D32 | semidirect |
| 68. C22×C32 | D53 | semidirect |
| 86. C53 | #13694 | semidirect |
| 99. C32 | C22⋊D53 | semidirect |
| 132. C22 | D1696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1696 | 2 |
| #20276801 | 2 |
| #20272915 | 2 |
| #20272894 | 2 |
| C22×C32×C53 | 2 |
| #13694 | 53 |