Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20277623 | C2 | semidirect |
| 3. #20273274 | C2 | semidirect |
| 4. #20273211 | C2 | semidirect |
| 5. #20273105 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 13. #16810829 | C4 | semidirect |
| 14. #16810819 | C4 | semidirect |
| 37. #13133217 | C2×C4 | semidirect |
| 38. #13133214 | C2×C4 | semidirect |
| 69. C4⋊C8×C53 | C2×C4 | semidirect |
| 214. #1286 | D53 | semidirect |
| 243. C53 | #9179 | semidirect |
| 277. C4⋊C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284181 | 2 |
| #20277623 | 2 |
| #20273274 | 2 |
| #20273211 | 2 |
| #20273105 | 2 |
| #20272616 | 2 |
| C53×#1286 | 2 |
| #9179 | 53 |