Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 11. Q16×#6157 | C4 | semidirect |
| 17. #16811536 | C4 | semidirect |
| 23. #16810428 | C4 | semidirect |
| 24. #16810427 | C4 | semidirect |
| 25. #16810426 | C4 | semidirect |
| 26. C53×#358 | C4 | semidirect |
| 91. Q16×C53 | C42 | semidirect |
| 100. Dic212 | C42 | semidirect |
| 196. #358 | #6157 | semidirect |
| 199. C53 | #12638 | semidirect |
| 256. Q16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#6157 | 2 |
| C2×#16811536 | 2 |
| C2×#16811510 | 2 |
| #107×#6157 | 2 |
| #20289773 | 2 |
| #20289772 | 2 |
| #358×D53 | 2 |
| #12638 | 53 |