Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
160 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276997 | C2 | semidirect |
| 2. #20272922 | C2 | semidirect |
| 3. #20272913 | C2 | semidirect |
| 21. Q32×C53 | Q8 | semidirect |
| 23. D16×C53 | Q8 | semidirect |
| 83. C53 | #13710 | semidirect |
| 87. Q32 | Dic106 | semidirect |
| 89. D16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276997 | 2 |
| #20272922 | 2 |
| #20272913 | 2 |
| #20272902 | 2 |
| C53×#2178 | 2 |
| #13710 | 53 |