Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. C2×#16810452 | C2 | semidirect |
| 4. #20275505 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 15. #16810430 | C4 | semidirect |
| 164. C53 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810452 | 2 |
| #20276443 | 2 |
| C2×#16810430 | 2 |
| #20275505 | 2 |
| #20272826 | 2 |
| #20272804 | 2 |
| C53×#2957 | 2 |
| #12947 | 53 |