Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
340 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. #20287728 | C2 | semidirect |
| 3. #20276756 | C2 | semidirect |
| 4. #20274075 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 140. Q8⋊C16 | D53 | semidirect |
| 164. C53 | #12329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287728 | 2 |
| #20276965 | 2 |
| #20276756 | 2 |
| #20274075 | 2 |
| #20272762 | 2 |
| #20272680 | 2 |
| C53×Q8⋊C16 | 2 |
| #12329 | 53 |