Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276497 | C2 | semidirect |
| 4. #20272816 | C2 | semidirect |
| 8. C2×#13133157 | C4 | semidirect |
| 10. C22×#11719908 | C4 | semidirect |
| 125. C53 | #12839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811040 | 2 |
| #20276497 | 2 |
| #20274761 | 2 |
| #20272816 | 2 |
| C53×#1812 | 2 |
| #12839 | 53 |