Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20291684 | C2 | semidirect |
| 2. #20290957 | C2 | semidirect |
| 3. C2×#16811522 | C2 | semidirect |
| 4. #20290945 | C2 | semidirect |
| 5. #20289769 | C2 | semidirect |
| 6. #20289765 | C2 | semidirect |
| 204. C53 | #12979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291684 | 2 |
| #20290957 | 2 |
| C2×#16811522 | 2 |
| #20290945 | 2 |
| #20289769 | 2 |
| #20289765 | 2 |
| #20283614 | 2 |
| #12979 | 53 |