Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20276518 | C2 | semidirect |
| 3. #20272656 | C2 | semidirect |
| 5. C53×#2163 | C2 | semidirect |
| 139. #2163 | D53 | semidirect |
| 164. C53 | #11463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283357 | 2 |
| #20276518 | 2 |
| #20272656 | 2 |
| #20272640 | 2 |
| C53×#2163 | 2 |
| #11463 | 53 |