Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16811059 | C2 | semidirect |
| 3. C2×#16810998 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. #20275601 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 38. C2×Dic212 | D4 | semidirect |
| 46. C2×D424 | D4 | semidirect |
| 59. #13133157 | D4 | semidirect |
| 75. M32×C53 | D4 | semidirect |
| 203. C2×#361 | D53 | semidirect |
| 236. C53 | #13331 | semidirect |
| 276. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811061 | 2 |
| C2×#16811059 | 2 |
| C2×#16810998 | 2 |
| C2×#16810435 | 2 |
| #20275601 | 2 |
| #20272796 | 2 |
| C2×C53×#361 | 2 |
| #13331 | 53 |