Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20291594 | C2 | semidirect |
| 2. #20290142 | C2 | semidirect |
| 3. #20290120 | C2 | semidirect |
| 4. #20289990 | C2 | semidirect |
| 5. #20289619 | C2 | semidirect |
| 6. #20289586 | C2 | semidirect |
| 26. #16810951 | C4 | semidirect |
| 28. #16810937 | C4 | semidirect |
| 32. #16810757 | C4 | semidirect |
| 34. C53×#450 | C4 | semidirect |
| 240. #450 | #6157 | semidirect |
| 260. C53 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291594 | 2 |
| #20290142 | 2 |
| #20290120 | 2 |
| #20289990 | 2 |
| #20289619 | 2 |
| #20289586 | 2 |
| #20285532 | 2 |
| #9332 | 53 |