Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20276996 | C2 | semidirect |
| 3. #20272922 | C2 | semidirect |
| 4. #20272912 | C2 | semidirect |
| 7. C53×#1426 | C2 | semidirect |
| 22. Dic424 | Q8 | semidirect |
| 24. D848 | Q8 | semidirect |
| 78. #1426 | D53 | semidirect |
| 96. C53 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276996 | 2 |
| #20276595 | 2 |
| #20272922 | 2 |
| #20272912 | 2 |
| #20272903 | 2 |
| #20272901 | 2 |
| C53×#1426 | 2 |
| #13710 | 53 |