Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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 | C22×D4×C13 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | C22×D4 | #261 |
| hypocenter | C13 | #2973 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719169 | C2 | semidirect |
| 3. C2×C22⋊#1057 | C2 | semidirect |
| 4. #11719144 | C2 | semidirect |
| 5. #11719128 | C2 | semidirect |
| 9. C2×#6122 | C22 | semidirect |
| 10. C22×#1057 | C22 | semidirect |
| 18. C22⋊#1057 | C22 | semidirect |
| 19. C22⋊#1057 | C22 | semidirect |
| 20. #88112 | C22 | semidirect |
| 21. #88110 | C22 | semidirect |
| 51. C23×C13 | M16 | semidirect |
| 140. C13 | #2973 | semidirect |
| 146. C23 | #6122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic13 | 2 |
| #11719169 | 2 |
| C2×C22⋊#1057 | 2 |
| #11719144 | 2 |
| #11719128 | 2 |
| #2973 | 13 |