Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291172 | C2 | semidirect |
| 2. #20290849 | C2 | semidirect |
| 3. #20290095 | C2 | semidirect |
| 4. #20290041 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 25. #16810904 | C4 | semidirect |
| 26. #16810903 | C4 | semidirect |
| 27. #16810815 | C4 | semidirect |
| 32. C53×#459 | C4 | semidirect |
| 131. C4×#6157 | D8 | semidirect |
| 270. #459 | #6157 | semidirect |
| 288. C53 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291172 | 2 |
| #20290849 | 2 |
| #20290095 | 2 |
| #20290041 | 2 |
| #20289612 | 2 |
| #20289542 | 2 |
| #20284714 | 2 |
| #9237 | 53 |