Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 2. #20291071 | C2 | semidirect |
| 3. C2×#16811551 | C2 | semidirect |
| 5. #20289796 | C2 | semidirect |
| 6. #20289777 | C2 | semidirect |
| 25. #16810408 | C4 | semidirect |
| 26. #16810407 | C4 | semidirect |
| 27. #16810406 | C4 | semidirect |
| 28. C53×#350 | C4 | semidirect |
| 201. #350 | #6157 | semidirect |
| 203. C53 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291377 | 2 |
| #20291071 | 2 |
| C2×#16811551 | 2 |
| #20290602 | 2 |
| #20289796 | 2 |
| #20289777 | 2 |
| #350×D53 | 2 |
| #12927 | 53 |