Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16810450 | C2 | semidirect |
| 5. #20272825 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#1952 | C2 | semidirect |
| 18. #16810429 | C4 | semidirect |
| 45. C2×#11719908 | C2×C4 | semidirect |
| 56. #108×C53 | C2×C4 | semidirect |
| 158. #1952 | D53 | semidirect |
| 185. C53 | #12946 | semidirect |
| 212. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283592 | 2 |
| C2×#16810450 | 2 |
| C2×#16810429 | 2 |
| #20276425 | 2 |
| #20272825 | 2 |
| #20272804 | 2 |
| C53×#1952 | 2 |
| #12946 | 53 |