Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×Dic212 | C2 | semidirect |
| 5. #20272772 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 78. Dic212 | SD16 | semidirect |
| 86. Q8×C53 | SD32 | semidirect |
| 129. Q8⋊C16 | D53 | semidirect |
| 152. C53 | #12354 | semidirect |
| 218. Q8 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic212 | 2 |
| #20276939 | 2 |
| #20276756 | 2 |
| #20274075 | 2 |
| #20272772 | 2 |
| #20272680 | 2 |
| C53×Q8⋊C16 | 2 |
| #12354 | 53 |