Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
460 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C24×C13 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C13×#483 | C2 | direct (N × H) |
| 4. C2×C13×#106 | C2 | semidirect |
| 5. C2×C13×#103 | C2 | semidirect |
| 20. C13×#106 | C22 | semidirect |
| 21. C13×#103 | C22 | semidirect |
| 46. C2×#483 | C13 | direct (N × H) |
| 71. #483 | C2×C13 | direct (N × H) |
| 72. C2×#106 | C2×C13 | semidirect |
| 73. C2×#103 | C2×C13 | semidirect |
| 102. #106 | C22×C13 | semidirect |
| 103. #103 | C22×C13 | semidirect |
| 106. C2×C13 | #483 | direct (N × H) |
| 133. C13 | C2×#483 | direct (N × H) |
| 171. C2 | C13×#483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C22⋊Q8 | 2 |
| C22×C13×C4⋊C4 | 2 |
| C13×#483 | 2 |
| C2×C13×#106 | 2 |
| C2×C13×#103 | 2 |
| C2×C13×C22⋊C8 | 2 |
| C2×#483 | 13 |