Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
220 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 220 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. C2×#16810460 | C2 | semidirect |
| 3. Q32×Dic53 | C2 | semidirect |
| 4. #20272910 | C2 | semidirect |
| 5. #20272894 | C2 | semidirect |
| 6. #20272893 | C2 | semidirect |
| 7. C2×C53×SD64 | C2 | semidirect |
| 36. Q32×C53 | D4 | semidirect |
| 93. Dic53 | SD64 | semidirect |
| 95. C2×SD64 | D53 | semidirect |
| 119. C53 | #13686 | semidirect |
| 127. Q32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810460 | 2 |
| #20276963 | 2 |
| Q32×Dic53 | 2 |
| #20272910 | 2 |
| #20272894 | 2 |
| #20272893 | 2 |
| C2×C53×SD64 | 2 |
| #13686 | 53 |