Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 3. #20290926 | C2 | semidirect |
| 4. #20289766 | C2 | semidirect |
| 8. C2×#13133291 | C4 | semidirect |
| 11. C22×#11719910 | C4 | semidirect |
| 13. #16811519 | C4 | semidirect |
| 127. C53 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811681 | 2 |
| #20290951 | 2 |
| #20290926 | 2 |
| #20289766 | 2 |
| #20274518 | 2 |
| #12613 | 53 |