Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 136 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×#16811509 | C2 | semidirect |
| 2. C2×#16811486 | C2 | semidirect |
| 3. #20289670 | C2 | direct (N × H) |
| 8. #16811509 | C22 | semidirect |
| 10. #16811486 | C22 | semidirect |
| 29. C2×D424 | C8 | semidirect |
| 80. D424 | C2×C8 | semidirect |
| 134. C2×C53 | #1331 | semidirect |
| 154. C53 | C2×#1331 | semidirect |
| 265. C2 | #20289670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811509 | 2 |
| C2×#16811486 | 2 |
| #20289670 | 2 |
| C2×#16810705 | 2 |
| C2×#1331 | 53 |