Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20285929 | C2 | semidirect |
| 4. #20275696 | C2 | semidirect |
| 6. #20272625 | C2 | semidirect |
| 7. C53×#1506 | C2 | semidirect |
| 191. #1506 | D53 | semidirect |
| 224. C53 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286098 | 2 |
| #20285929 | 2 |
| #20285728 | 2 |
| #20275696 | 2 |
| #20273222 | 2 |
| #20272625 | 2 |
| C53×#1506 | 2 |
| #10215 | 53 |