Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 590 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. #20285111 | C2 | semidirect |
| 3. #20280827 | C2 | semidirect |
| 4. #20273314 | C2 | semidirect |
| 5. #20273224 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1556 | C2 | semidirect |
| 190. #1556 | D53 | semidirect |
| 223. C53 | #10094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285704 | 2 |
| #20285111 | 2 |
| #20280827 | 2 |
| #20273314 | 2 |
| #20273224 | 2 |
| #20272607 | 2 |
| C53×#1556 | 2 |
| #10094 | 53 |