Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20276452 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. #20274761 | C2 | semidirect |
| 5. C53×#2115 | C2 | semidirect |
| 11. C2×#13133239 | C4 | semidirect |
| 13. C22×D424 | C4 | semidirect |
| 15. #16810661 | C22 | semidirect |
| 21. C2×M32×C53 | C22 | semidirect |
| 172. #2115 | D53 | semidirect |
| 190. C2×M32 | C2×D53 | semidirect |
| 197. C53 | #12741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811428 | 2 |
| #20276452 | 2 |
| #20276432 | 2 |
| #20274761 | 2 |
| C53×#2115 | 2 |
| #12741 | 53 |