Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
644 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 237 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 | #2857 |
| 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 |
|---|---|---|
| 3. C2×#88123 | C2 | semidirect |
| 5. #11718596 | C2 | semidirect |
| 6. #11718590 | C2 | semidirect |
| 7. #11718589 | C2 | semidirect |
| 29. C22×C4×C13 | Q8 | semidirect |
| 85. C22×C13 | C4⋊Q8 | semidirect |
| 94. C4×C13 | C22⋊Q8 | semidirect |
| 128. C22×C4 | Dic26 | semidirect |
| 142. C13 | #2857 | semidirect |
| 173. C22 | #88123 | semidirect |
| 183. C4 | #88178 | 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×#88178 | 2 |
| C2×#88123 | 2 |
| #11718873 | 2 |
| #11718596 | 2 |
| #11718590 | 2 |
| #11718589 | 2 |
| #2857 | 13 |