Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
556 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C22×C42×C13 | C2 |
| prime radical | C24×C13 | C23 |
| hypercenter | C22×C42 | D13 |
| hypocenter | C13 | #2851 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#88124 | C2 | semidirect |
| 5. #11718597 | C2 | semidirect |
| 6. #11718594 | C2 | semidirect |
| 7. #11718589 | C2 | semidirect |
| 82. C22×C13 | #125 | semidirect |
| 136. C13 | #2851 | semidirect |
| 167. C22 | #88124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C13 | 2 |
| C2×#88124 | 2 |
| #11718873 | 2 |
| #11718871 | 2 |
| #11718597 | 2 |
| #11718594 | 2 |
| #11718589 | 2 |
| #2851 | 13 |