Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C13×#384 | C2 |
| prime radical | C2×#88149 | C2 |
| hypercenter | #384 | D13 |
| hypocenter | C13 | #2620 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88151 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C2×#88126 | C2 | semidirect |
| 5. C13×#384 | C2 | semidirect |
| 6. #11718655 | C2 | semidirect |
| 7. #11718652 | C2 | semidirect |
| 8. #11718649 | C2 | semidirect |
| 9. #11718635 | C2 | semidirect |
| 54. C42×C13 | D4 | semidirect |
| 106. #384 | D13 | semidirect |
| 188. C42 | D52 | semidirect |
| 189. C13 | #2620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88151 | 2 |
| C2×#88149 | 2 |
| C2×#88129 | 2 |
| C2×#88126 | 2 |
| C13×#384 | 2 |
| #11718655 | 2 |
| #11718652 | 2 |
| #11718649 | 2 |
| #11718635 | 2 |
| #2620 | 13 |