Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2186 conjugacy classes of subgroups; only the 683 normal subgroups are shown.
This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 683 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. #20283107 | C2 | direct (N × H) |
| 3. C2×#16810507 | C2 | semidirect |
| 4. C2×C43×C53 | C2 | semidirect |
| 8. #16810507 | C22 | semidirect |
| 11. C43×C53 | C22 | semidirect |
| 54. C2×C43 | D53 | semidirect |
| 55. C2×C53 | #2866 | semidirect |
| 64. C43 | C2×D53 | semidirect |
| 65. C53 | C2×#2866 | semidirect |
| 105. C2 | #20283107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283107 | 2 |
| C2×#16810514 | 2 |
| C2×#16810507 | 2 |
| C2×C43×C53 | 2 |
| C2×#2866 | 53 |