Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C2×#16811041 | C2 | semidirect |
| 3. C2×#16810430 | C2 | semidirect |
| 4. #20274766 | C2 | semidirect |
| 5. #20272827 | C2 | semidirect |
| 6. #20272810 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 15. #16810895 | C4 | semidirect |
| 16. #16810890 | C4 | semidirect |
| 177. #2145 | D53 | semidirect |
| 209. C53 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811041 | 2 |
| #20284431 | 2 |
| C2×#16810430 | 2 |
| #20274766 | 2 |
| #20272827 | 2 |
| #20272810 | 2 |
| C53×#2145 | 2 |
| #13071 | 53 |