Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20277027 | C2 | semidirect |
| 2. #20276963 | C2 | semidirect |
| 3. #20276596 | C2 | semidirect |
| 4. #20272912 | C2 | semidirect |
| 5. #20272906 | C2 | semidirect |
| 6. #20272905 | C2 | semidirect |
| 7. C53×#2263 | C2 | semidirect |
| 37. Q32×C53 | D4 | semidirect |
| 41. D16×C53 | D4 | semidirect |
| 96. #2263 | D53 | semidirect |
| 122. C53 | #13692 | semidirect |
| 129. Q32 | C22⋊D53 | semidirect |
| 136. D16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277027 | 2 |
| #20276963 | 2 |
| #20276596 | 2 |
| #20272912 | 2 |
| #20272906 | 2 |
| #20272905 | 2 |
| C53×#2263 | 2 |
| #13692 | 53 |