Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#16810680 | C2 | semidirect |
| 3. C2×#16810362 | C2 | semidirect |
| 4. #20272597 | C2 | semidirect |
| 5. C53×#1749 | C2 | semidirect |
| 45. #13133128 | D4 | semidirect |
| 201. #1749 | D53 | semidirect |
| 232. C53 | #9123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810680 | 2 |
| #20283016 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| C53×#1749 | 2 |
| #9123 | 53 |