Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 1. #20291682 | C2 | semidirect |
| 2. #20290951 | C2 | semidirect |
| 3. #20290942 | C2 | semidirect |
| 4. #20289765 | C2 | semidirect |
| 28. C2×#11719910 | D4 | semidirect |
| 162. C53 | #12981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| #20290951 | 2 |
| #20290942 | 2 |
| #20289765 | 2 |
| #20283410 | 2 |
| #12981 | 53 |