Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276868 | C2 | semidirect |
| 4. #20274119 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 128. Q8⋊C16 | D53 | semidirect |
| 151. C53 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287728 | 2 |
| #20276939 | 2 |
| #20276868 | 2 |
| #20274119 | 2 |
| #20272762 | 2 |
| #20272680 | 2 |
| C53×Q8⋊C16 | 2 |
| #12385 | 53 |