Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×#564 | C2 |
| prime radical | C22×D13 | C24 |
| hypercenter | #564 | D13 |
| hypocenter | C13 | #3556 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#564 | C2 | semidirect |
| 4. C13⋊#564 | C2 | semidirect |
| 5. #11719390 | C2 | semidirect |
| 49. #564 | D13 | semidirect |
| 95. C13 | #3556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#564 | 2 |
| #11719401 | 2 |
| #11719393 | 2 |
| C13⋊#564 | 2 |
| #11719390 | 2 |
| #3556 | 13 |