Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical | C2×C13×#120 | C2 |
| hypercenter | C2×#120 | D13 |
| hypocenter | C13 | #2849 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic13 | C2 | semidirect |
| 3. C2×#88189 | C2 | semidirect |
| 4. #11718908 | C2 | semidirect |
| 5. #11718881 | C2 | semidirect |
| 6. #11718607 | C2 | semidirect |
| 7. #11718604 | C2 | semidirect |
| 20. C2×C22⋊Dic13 | C22 | semidirect |
| 22. C2×#6101 | C22 | semidirect |
| 23. #88071 | C22 | semidirect |
| 41. C22×Dic13 | D4 | semidirect |
| 95. C22×C13 | #123 | semidirect |
| 151. C13 | #2849 | semidirect |
| 188. C22 | #88189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic13 | 2 |
| C2×C13×#120 | 2 |
| C2×#88189 | 2 |
| #11718908 | 2 |
| #11718881 | 2 |
| #11718607 | 2 |
| #11718604 | 2 |
| #2849 | 13 |