Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#16811681 | C2 | semidirect |
| 2. #20290957 | C2 | semidirect |
| 3. C2×#16811522 | C2 | semidirect |
| 4. #20290953 | C2 | semidirect |
| 5. #20289769 | C2 | semidirect |
| 6. #20289765 | C2 | semidirect |
| 210. C53 | #12987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811681 | 2 |
| #20290957 | 2 |
| C2×#16811522 | 2 |
| #20290953 | 2 |
| #20289769 | 2 |
| #20289765 | 2 |
| #20283614 | 2 |
| #12987 | 53 |