Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting, prime radical | C13×#121 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | #121 | #261 |
| hypocenter | C13 | #2967 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719145 | C2 | semidirect |
| 3. #11719144 | C2 | semidirect |
| 4. #11719144 | C2 | semidirect |
| 5. #11719128 | C2 | semidirect |
| 6. C4×#6122 | C2 | semidirect |
| 7. #11719078 | C2 | semidirect |
| 8. #11719068 | C2 | semidirect |
| 9. #11719062 | C2 | semidirect |
| 178. C13 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719305 | 2 |
| #11719145 | 2 |
| #11719144 | 2 |
| #11719128 | 2 |
| C4×#6122 | 2 |
| #11719078 | 2 |
| #11719068 | 2 |
| #11719062 | 2 |
| #2967 | 13 |