Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4⋊#11719910 | C2 | semidirect |
| 2. C2×#16811511 | C2 | semidirect |
| 3. #20289668 | C2 | direct (N × H) |
| 8. C4⋊#11719910 | C22 | semidirect |
| 10. #16811511 | C22 | semidirect |
| 131. C2×C53 | #1330 | semidirect |
| 151. C53 | C2×#1330 | semidirect |
| 259. C2 | #20289668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11719910 | 2 |
| C2×#16811511 | 2 |
| #20289668 | 2 |
| C2×#16810700 | 2 |
| C2×#1330 | 53 |