Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 88 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×#16811520 | C2 | semidirect |
| 2. C2×#16811492 | C2 | semidirect |
| 3. #20289689 | C2 | direct (N × H) |
| 8. #16811520 | C22 | semidirect |
| 10. #16811492 | C22 | semidirect |
| 175. C2×C53 | #1341 | semidirect |
| 194. C53 | C2×#1341 | semidirect |
| 347. C2 | #20289689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811520 | 2 |
| C2×#16811492 | 2 |
| #20289689 | 2 |
| C2×#16810873 | 2 |
| C2×#1341 | 53 |