Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
506 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #20289704 | C2 | direct (N × H) |
| 11. C22×Dic212 | C4 | semidirect |
| 16. #16810865 | C4 | semidirect |
| 19. C2×#107×C53 | C4 | semidirect |
| 31. C2×Dic212 | C2×C4 | semidirect |
| 49. #107×C53 | C2×C4 | semidirect |
| 152. C2×C53 | #1348 | semidirect |
| 168. C2×#107 | #6157 | semidirect |
| 174. C53 | C2×#1348 | semidirect |
| 202. #107 | C2×#6157 | semidirect |
| 305. C2 | #20289704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811518 | 2 |
| C2×#16811497 | 2 |
| #20289704 | 2 |
| C2×#16810865 | 2 |
| C2×#1348 | 53 |