Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20272919 | C2 | semidirect |
| 4. #20272908 | C2 | semidirect |
| 5. C2×C53×Q64 | C2 | semidirect |
| 64. C2×Q64 | D53 | semidirect |
| 83. C53 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277008 | 2 |
| #20276837 | 2 |
| #20272919 | 2 |
| #20272908 | 2 |
| C2×C53×Q64 | 2 |
| #13701 | 53 |