Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. #20291071 | C2 | semidirect |
| 4. #20290835 | C2 | semidirect |
| 5. #20289774 | C2 | semidirect |
| 6. #20289771 | C2 | semidirect |
| 25. #16810440 | C4 | semidirect |
| 26. #16810438 | C4 | semidirect |
| 27. #16810436 | C4 | semidirect |
| 28. C53×#361 | C4 | semidirect |
| 187. #361 | #6157 | semidirect |
| 190. C53 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291491 | 2 |
| #20291071 | 2 |
| C2×#16811537 | 2 |
| #20290835 | 2 |
| #20289774 | 2 |
| #20289771 | 2 |
| #20276461 | 2 |
| #12942 | 53 |