Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
128 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #102 |
| commutator | C8 | C42×C13 |
| Frattini, cosocle | C22×C8 | C22×C13 |
| socle | C2×C13 | #340 |
| prime radical | C23×C13 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C13×M32 | C4 | semidirect |
| 11. C13×#108 | C4 | semidirect |
| 28. #1389 | C13 | direct (N × H) |
| 58. M32 | C4×C13 | semidirect |
| 61. #108 | C4×C13 | semidirect |
| 82. C13 | #1389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×M32 | 2 |
| C2×C13×#108 | 2 |
| C13×#427 | 2 |
| #1389 | 13 |