Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C13 |
| prime radical | C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#499 | C2 | semidirect |
| 3. C13×#365 | C2 | semidirect |
| 4. C13×#364 | C2 | semidirect |
| 28. #2231 | C13 | direct (N × H) |
| 41. #499 | C2×C13 | semidirect |
| 43. #365 | C2×C13 | semidirect |
| 44. #364 | C2×C13 | semidirect |
| 78. C13 | #2231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#499 | 2 |
| C13×#443 | 2 |
| C13×#365 | 2 |
| C13×#364 | 2 |
| C13×#360 | 2 |
| #2231 | 13 |