Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16810447 | C2 | semidirect |
| 5. #20272820 | C2 | semidirect |
| 6. #20272795 | C2 | semidirect |
| 7. C53×#1773 | C2 | semidirect |
| 16. #16810423 | C4 | semidirect |
| 137. #1773 | D53 | semidirect |
| 159. C53 | #13142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810447 | 2 |
| C2×#16810435 | 2 |
| #20276430 | 2 |
| #20275591 | 2 |
| #20272820 | 2 |
| #20272795 | 2 |
| C53×#1773 | 2 |
| #13142 | 53 |