Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 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 | C22×C13 | C23×C4 |
| Fitting | C13×#390 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C2×#88194 | C2 |
| hypercenter | #390 | D13 |
| hypocenter | C13 | #2328 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic13 | C2 | semidirect |
| 3. C2×#88147 | C2 | semidirect |
| 4. C13×#390 | C2 | semidirect |
| 5. #11718638 | C2 | semidirect |
| 6. #11718619 | C2 | semidirect |
| 7. #11718617 | C2 | semidirect |
| 8. #11718600 | C2 | semidirect |
| 9. #11718593 | C2 | semidirect |
| 19. #88194 | C4 | semidirect |
| 34. C2×D4×C13 | C2×C4 | semidirect |
| 40. C2×C22⋊D13 | C2×C4 | semidirect |
| 49. C2×D52 | C2×C4 | semidirect |
| 59. C4×Dic13 | C2×C4 | semidirect |
| 60. C4×Dic13 | D4 | semidirect |
| 99. #390 | D13 | semidirect |
| 163. C2×D4 | C4×D13 | semidirect |
| 184. C13 | #2328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88194 | 2 |
| C2×D4×Dic13 | 2 |
| C2×#88147 | 2 |
| C13×#390 | 2 |
| #11718638 | 2 |
| #11718619 | 2 |
| #11718617 | 2 |
| #11718600 | 2 |
| #11718593 | 2 |
| #2328 | 13 |