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. #20290119 | C2 | semidirect |
| 4. #20290106 | C2 | semidirect |
| 5. #20290096 | C2 | semidirect |
| 6. #20290088 | C2 | semidirect |
| 21. #16811358 | C4 | semidirect |
| 22. #16811334 | C4 | semidirect |
| 23. #16811295 | C4 | semidirect |
| 31. Q82×C53 | C4 | semidirect |
| 192. Q82 | #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 |
| #20290119 | 2 |
| #20290106 | 2 |
| #20290096 | 2 |
| #20290088 | 2 |
| #20288801 | 2 |
| #17550 | 53 |