Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20276475 | C2 | semidirect |
| 4. #20274838 | C2 | semidirect |
| 5. #20272827 | C2 | semidirect |
| 6. #20272810 | C2 | semidirect |
| 10. #16810745 | C4 | semidirect |
| 164. C53 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283632 | 2 |
| #20276475 | 2 |
| C2×#16810430 | 2 |
| #20274838 | 2 |
| #20272827 | 2 |
| #20272810 | 2 |
| C53×#2145 | 2 |
| #12830 | 53 |