Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285097 | C2 | semidirect |
| 4. #20273440 | C2 | semidirect |
| 6. #20272608 | C2 | semidirect |
| 7. C53×#1506 | C2 | semidirect |
| 180. #1506 | D53 | semidirect |
| 210. C53 | #10098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285714 | 2 |
| #20285097 | 2 |
| #20280651 | 2 |
| #20273440 | 2 |
| #20273314 | 2 |
| #20272608 | 2 |
| C53×#1506 | 2 |
| #10098 | 53 |