Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 23. #16810375 | C4 | semidirect |
| 24. #16810375 | C4 | semidirect |
| 25. #16810374 | C4 | semidirect |
| 26. C53×#334 | C4 | semidirect |
| 165. #334 | #6157 | semidirect |
| 166. C53 | #9632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290639 | 2 |
| #20290509 | 2 |
| #20290285 | 2 |
| #20290283 | 2 |
| #20289612 | 2 |
| #20273460 | 2 |
| #9632 | 53 |