Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
278 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #99 |
| commutator | C23 | C22×C4×C13 |
| Frattini, cosocle | C2×D4 | C23×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×#352 | C2 | direct (N × H) |
| 6. C23×C4×C13 | C4 | semidirect |
| 10. C13×#123 | C4 | semidirect |
| 15. C2×C13×C22⋊C4 | C4 | semidirect |
| 34. C22×C4×C13 | C2×C4 | semidirect |
| 46. C13×C22⋊C4 | C2×C4 | semidirect |
| 47. C2×#352 | C13 | direct (N × H) |
| 80. #352 | C2×C13 | direct (N × H) |
| 103. C23×C4 | C4×C13 | semidirect |
| 107. #123 | C4×C13 | semidirect |
| 112. C2×C22⋊C4 | C4×C13 | semidirect |
| 123. C2×C13 | #352 | direct (N × H) |
| 139. C22×C4 | C2×C4×C13 | semidirect |
| 151. C22⋊C4 | C2×C4×C13 | semidirect |
| 152. C13 | C2×#352 | direct (N × H) |
| 209. C2 | C13×#352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#123 | 2 |
| C2×C13×#100 | 2 |
| C2×C13×#99 | 2 |
| C13×#352 | 2 |
| C2×#352 | 13 |