Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D13 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting, prime radical | C13×#525 | C2 |
| cosocle | C2×C4×C13 | C24 |
| hypercenter | #525 | D13 |
| hypocenter | C13 | #2977 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11718895 | C2 | semidirect |
| 3. C2×C22⋊#1055 | C2 | semidirect |
| 4. #11718672 | C2 | semidirect |
| 5. D4×#1055 | C2 | semidirect |
| 6. #11718661 | C2 | semidirect |
| 15. C2×#6099 | C22 | semidirect |
| 17. C22×#1055 | C22 | semidirect |
| 21. C22⋊#1055 | C22 | semidirect |
| 22. C4⋊#1055 | C22 | semidirect |
| 23. #88043 | C22 | semidirect |
| 24. C4×#1055 | C22 | semidirect |
| 137. C13 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#525 | 2 |
| #11718895 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718672 | 2 |
| D4×#1055 | 2 |
| #11718661 | 2 |
| #2977 | 13 |