Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1030 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 226 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. #20291617 | C2 | semidirect |
| 2. #20291155 | C2 | semidirect |
| 3. #20290117 | C2 | semidirect |
| 4. #20290104 | C2 | semidirect |
| 5. #20290095 | C2 | semidirect |
| 6. #20290086 | C2 | semidirect |
| 21. #16811359 | C4 | semidirect |
| 22. Q8×Dic106 | C4 | semidirect |
| 23. #16811330 | C4 | semidirect |
| 31. C53×#550 | C4 | semidirect |
| 194. #550 | #6157 | semidirect |
| 215. C53 | #17550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291617 | 2 |
| #20291155 | 2 |
| #20290117 | 2 |
| #20290104 | 2 |
| #20290095 | 2 |
| #20290086 | 2 |
| #20288795 | 2 |
| #17550 | 53 |