Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #20273317 | C2 | semidirect |
| 5. #20272584 | C2 | semidirect |
| 6. #20272564 | C2 | semidirect |
| 7. C53×#1470 | C2 | semidirect |
| 201. #1470 | D53 | semidirect |
| 236. C53 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810920 | 2 |
| #20283749 | 2 |
| #20273317 | 2 |
| #20273157 | 2 |
| #20272584 | 2 |
| #20272564 | 2 |
| C53×#1470 | 2 |
| #9245 | 53 |