Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
252 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C24×C13 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#432 | C2 | semidirect |
| 3. C13×#324 | C2 | semidirect |
| 37. #1464 | C13 | direct (N × H) |
| 63. #432 | C2×C13 | semidirect |
| 64. #324 | C2×C13 | semidirect |
| 121. C13 | #1464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#117 | 2 |
| C13×#432 | 2 |
| C13×#324 | 2 |
| C13×#323 | 2 |
| #1464 | 13 |