Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 2. C2×#16811515 | C2 | semidirect |
| 3. C2×#16811515 | C2 | semidirect |
| 4. #20289765 | C2 | semidirect |
| 8. #16811521 | C4 | semidirect |
| 27. #13133291 | C2×C4 | semidirect |
| 29. C2×#11719910 | C2×C4 | semidirect |
| 171. C53 | #12609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290957 | 2 |
| C2×#16811515 | 2 |
| #20289765 | 2 |
| #20283143 | 2 |
| #12609 | 53 |