Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
280 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4 | C22×D13 |
| commutator, socle, prime radical | C23×C13 | C22×C4 |
| Fitting | C13×#336 | C2 |
| cosocle | C22×C4×C13 | C23 |
| hypercenter | #336 | D13 |
| hypocenter | C13 | #1985 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 38. C2×C8×C13 | Q8 | semidirect |
| 53. C2×#1055 | Q8 | semidirect |
| 152. C2×C8 | Dic26 | semidirect |
| 162. C13 | #1985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic26 | 2 |
| C2×#88055 | 2 |
| C2×#88054 | 2 |
| C13×#336 | 2 |
| #11718142 | 2 |
| #11718116 | 2 |
| #1985 | 13 |