Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20272821 | C2 | semidirect |
| 4. #20272817 | C2 | semidirect |
| 9. #16810661 | C4 | semidirect |
| 12. C2×#13133149 | C4 | semidirect |
| 136. C53 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283310 | 2 |
| #20274761 | 2 |
| #20272821 | 2 |
| #20272817 | 2 |
| C53×#2115 | 2 |
| #12873 | 53 |