Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#16810458 | C2 | semidirect |
| 3. #20276963 | C2 | semidirect |
| 4. #20276561 | C2 | semidirect |
| 5. #20272910 | C2 | semidirect |
| 6. #20272892 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 29. D848 | D4 | semidirect |
| 96. Dic53 | D32 | semidirect |
| 103. #1415 | D53 | semidirect |
| 123. C53 | #13685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1696 | 2 |
| C2×#16810458 | 2 |
| #20276963 | 2 |
| #20276561 | 2 |
| #20272910 | 2 |
| #20272892 | 2 |
| C53×#1415 | 2 |
| #13685 | 53 |