Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×#13133285 | C2 | semidirect |
| 3. #20290274 | C2 | semidirect |
| 4. #20289612 | C2 | semidirect |
| 15. #16810754 | C4 | semidirect |
| 16. #16810702 | C4 | semidirect |
| 17. #16810700 | C4 | semidirect |
| 24. C53×#446 | C4 | semidirect |
| 138. #88322 | #104 | semidirect |
| 171. #446 | #6157 | semidirect |
| 188. C53 | #8669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290588 | 2 |
| C4×#13133285 | 2 |
| #20290274 | 2 |
| #20289612 | 2 |
| #20283680 | 2 |
| #8669 | 53 |