Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C4×C13×#41 | C2 |
| prime radical | C2×C13×#41 | C22 |
| hypercenter | C4×#41 | D13 |
| hypocenter | C13 | #3504 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11719274 | C2 | semidirect |
| 4. #11719244 | C2 | semidirect |
| 5. #11719224 | C2 | semidirect |
| 6. #11719175 | C2 | semidirect |
| 7. C2×#88124 | C2 | semidirect |
| 28. C13×#41 | Q8 | semidirect |
| 102. #41 | Dic26 | semidirect |
| 123. C13 | #3504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#41 | 2 |
| #11719532 | 2 |
| #11719274 | 2 |
| #11719244 | 2 |
| #11719224 | 2 |
| #11719175 | 2 |
| C2×#88124 | 2 |
| #3504 | 13 |