Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1134 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 432 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. #20290642 | C2 | direct (N × H) |
| 21. C2×C42×C53 | C8 | semidirect |
| 37. C42×C53 | C2×C8 | semidirect |
| 71. C2×C53 | #1839 | semidirect |
| 82. C53 | C2×#1839 | semidirect |
| 93. C2×C42 | #88324 | semidirect |
| 112. C42 | C2×#88324 | semidirect |
| 139. C2 | #20290642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290642 | 2 |
| C2×#16811489 | 2 |
| C2×C42×Dic53 | 2 |
| C2×#1839 | 53 |