Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C23×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. C13×M16 | Q8 | semidirect |
| 34. C42×C13 | Q8 | semidirect |
| 35. #2061 | C13 | direct (N × H) |
| 91. M16 | Q8×C13 | semidirect |
| 102. C42 | Q8×C13 | semidirect |
| 103. C13 | #2061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#544 | 2 |
| C13×#428 | 2 |
| C13×#382 | 2 |
| C13×#343 | 2 |
| C13×#339 | 2 |
| #2061 | 13 |