Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1770 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 312 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×#16811568 | C2 | semidirect |
| 2. C2×C42×#6157 | C2 | semidirect |
| 4. #20289894 | C2 | semidirect |
| 12. C2×#13133212 | C4 | semidirect |
| 13. C2×#13133211 | C4 | semidirect |
| 14. C2×#13133210 | C4 | semidirect |
| 20. C2×#126×C53 | C4 | semidirect |
| 77. C42×C53 | C22⋊C4 | semidirect |
| 84. C4×Dic53 | C22⋊C4 | semidirect |
| 102. C2×#6157 | #126 | semidirect |
| 150. C2×#126 | #6157 | semidirect |
| 160. C53 | #14711 | semidirect |
| 224. C42 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| C2×C42×#6157 | 2 |
| #20289896 | 2 |
| #20289894 | 2 |
| C2×#126×D53 | 2 |
| #14711 | 53 |