Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291543 | C2 | semidirect |
| 2. #20290193 | C2 | semidirect |
| 3. C2×#16811478 | C2 | semidirect |
| 4. #20289985 | C2 | semidirect |
| 5. #20289610 | C2 | semidirect |
| 6. #20289554 | C2 | semidirect |
| 247. C53 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291543 | 2 |
| #20290193 | 2 |
| C2×#16811478 | 2 |
| #20289985 | 2 |
| #20289610 | 2 |
| #20289554 | 2 |
| #20285683 | 2 |
| #9265 | 53 |