Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16811061 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20275603 | C2 | semidirect |
| 5. C53×#1376 | C2 | semidirect |
| 26. C2×Dic212 | D4 | semidirect |
| 37. C2×D424 | D4 | semidirect |
| 50. M32×C53 | D4 | semidirect |
| 146. #1376 | D53 | semidirect |
| 168. C53 | #13331 | semidirect |
| 195. M32 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811061 | 2 |
| C2×#16811000 | 2 |
| C2×#16810437 | 2 |
| #20275603 | 2 |
| C53×#1376 | 2 |
| #13331 | 53 |