Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 195 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. C22×D848 | C2 | semidirect |
| 2. C22×C16×D53 | C2 | semidirect |
| 3. C2×#16810860 | C2 | semidirect |
| 4. #20276802 | C2 | direct (N × H) |
| 5. C2×#16810423 | C2 | semidirect |
| 6. C2×C53×#366 | C2 | semidirect |
| 11. C2×D848 | C22 | semidirect |
| 14. C2×C16×D53 | C22 | semidirect |
| 16. #16810860 | C22 | semidirect |
| 18. #16810423 | C22 | semidirect |
| 21. C53×#366 | C22 | semidirect |
| 44. C2×C16×C53 | D4 | semidirect |
| 78. C16×C53 | C2×D4 | semidirect |
| 87. C22×D53 | D16 | semidirect |
| 120. C2×D53 | C2×D16 | semidirect |
| 130. C2×#366 | D53 | semidirect |
| 132. C2×C53 | #2215 | semidirect |
| 151. #366 | C2×D53 | semidirect |
| 153. C53 | C2×#2215 | semidirect |
| 175. C2×C16 | D212 | semidirect |
| 211. C16 | C2×D212 | semidirect |
| 259. C2 | #20276802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C22×C16×D53 | 2 |
| C2×#16810860 | 2 |
| #20276802 | 2 |
| C2×#16810423 | 2 |
| C2×C53×#366 | 2 |
| C2×#2215 | 53 |