Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #20272920 | C2 | semidirect |
| 3. #20272913 | C2 | semidirect |
| 5. C53×#2254 | C2 | semidirect |
| 17. Dic424 | Q8 | semidirect |
| 19. D848 | Q8 | semidirect |
| 66. #2254 | D53 | semidirect |
| 83. C53 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276597 | 2 |
| #20272920 | 2 |
| #20272913 | 2 |
| #20272901 | 2 |
| C53×#2254 | 2 |
| #13710 | 53 |