Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
640 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20285861 | C2 | semidirect |
| 4. #20275692 | C2 | semidirect |
| 5. #20273386 | C2 | semidirect |
| 7. C53×#1276 | C2 | semidirect |
| 98. C42×C53 | SD16 | semidirect |
| 182. #1276 | D53 | semidirect |
| 209. C53 | #10294 | semidirect |
| 295. C42 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285861 | 2 |
| #20285658 | 2 |
| #20283072 | 2 |
| #20275692 | 2 |
| #20273386 | 2 |
| #20273382 | 2 |
| C53×#1276 | 2 |
| #10294 | 53 |