Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20291517 | C2 | semidirect |
| 3. C4×#13133280 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289546 | C2 | semidirect |
| 25. #16810909 | C4 | semidirect |
| 26. #16810908 | C4 | semidirect |
| 27. #16810820 | C4 | semidirect |
| 32. C53×#460 | C4 | semidirect |
| 118. #11719936 | SD16 | semidirect |
| 184. Dic106 | #104 | semidirect |
| 234. #460 | #6157 | semidirect |
| 253. C53 | #8992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291517 | 2 |
| #20290879 | 2 |
| C4×#13133280 | 2 |
| #20290061 | 2 |
| #20289612 | 2 |
| #20289546 | 2 |
| #20284745 | 2 |
| #8992 | 53 |