Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
640 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 338 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. C2×#88112 | C2 | direct (N × H) |
| 11. #88112 | C22 | direct (N × H) |
| 15. C22×Dic13 | C8 | semidirect |
| 33. C2×Dic13 | C2×C8 | semidirect |
| 43. C22×C13 | C4⋊C8 | semidirect |
| 50. Dic13 | C22×C8 | semidirect |
| 61. C2×C13 | C2×C4⋊C8 | semidirect |
| 78. C13 | C22×C4⋊C8 | semidirect |
| 93. C22 | #88112 | direct (N × H) |
| 103. C2 | C2×#88112 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1057 | 2 |
| C22×C4×Dic13 | 2 |
| C2×#88112 | 2 |
| C22×C4⋊C8 | 13 |