Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
166 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 4. C2×#13133149 | C4 | semidirect |
| 8. #16810388 | C4 | semidirect |
| 89. C53 | #7410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276160 | 2 |
| #20272653 | 2 |
| C53×#1391 | 2 |
| #7410 | 53 |