Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
708 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 124 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. #20290571 | C2 | semidirect |
| 2. C2×#16811489 | C2 | semidirect |
| 3. #20289532 | C2 | semidirect |
| 4. #20289531 | C2 | semidirect |
| 258. C53 | #7664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290571 | 2 |
| C2×#16811489 | 2 |
| #20289532 | 2 |
| #20289531 | 2 |
| #20283058 | 2 |
| #7664 | 53 |