Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 366 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. C2×#16810452 | C2 | semidirect |
| 3. C2×#16810448 | C2 | semidirect |
| 6. #20272824 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 10. #16811041 | C4 | semidirect |
| 147. #1387 | D53 | semidirect |
| 172. C53 | #12842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811041 | 2 |
| C2×#16810452 | 2 |
| C2×#16810448 | 2 |
| #20274780 | 2 |
| #20274776 | 2 |
| #20272824 | 2 |
| C53×#1387 | 2 |
| #12842 | 53 |