Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20276470 | C2 | semidirect |
| 5. #20274876 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 11. #16810717 | C4 | semidirect |
| 13. #16810705 | C4 | semidirect |
| 159. #1386 | D53 | semidirect |
| 182. C53 | #12817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283486 | 2 |
| #20276470 | 2 |
| C2×#16810434 | 2 |
| C2×#16810432 | 2 |
| #20274876 | 2 |
| #20272820 | 2 |
| C53×#1386 | 2 |
| #12817 | 53 |