Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q16×Dic106 | C2 | semidirect |
| 5. #20272774 | C2 | semidirect |
| 6. #20272695 | C2 | semidirect |
| 7. C53×#1332 | C2 | semidirect |
| 61. Q16×C53 | SD16 | semidirect |
| 103. Dic106 | SD32 | semidirect |
| 130. #1332 | D53 | semidirect |
| 152. C53 | #12354 | semidirect |
| 189. Q16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic106 | 2 |
| #20276939 | 2 |
| #20276755 | 2 |
| #20274076 | 2 |
| #20272774 | 2 |
| #20272695 | 2 |
| C53×#1332 | 2 |
| #12354 | 53 |