Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 82. #88324 | Q32 | semidirect |
| 122. C53 | #12072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290354 | 2 |
| #20290303 | 2 |
| #20289747 | 2 |
| #20289672 | 2 |
| #88324⋊C16 | 2 |
| #20276573 | 2 |
| #12072 | 53 |