Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 136 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×#16811512 | C2 | semidirect |
| 2. C2×#16811484 | C2 | semidirect |
| 3. #20289673 | C2 | direct (N × H) |
| 8. #16811512 | C22 | semidirect |
| 10. #16811484 | C22 | semidirect |
| 45. C2×D8×C53 | C8 | semidirect |
| 64. D8×C53 | C2×C8 | semidirect |
| 131. C2×C53 | #1333 | semidirect |
| 150. C53 | C2×#1333 | semidirect |
| 155. C2×D8 | #88324 | semidirect |
| 193. D8 | C2×#88324 | semidirect |
| 257. C2 | #20289673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811512 | 2 |
| C2×#16811484 | 2 |
| #20289673 | 2 |
| C2×D8×Dic53 | 2 |
| C2×#1333 | 53 |