Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
308 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92318⋊C2 |
| commutator, cosocle, hypocenter | #6903 | C23 |
| Frattini | C9 | C2×#1113 |
| Fitting | C2×#6903 | C22 |
| socle | C2×C3 | #66431 |
| LCS | G ▷ #6903 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92319 | C2 | semidirect |
| 2. C2×#92318 | C2 | semidirect |
| 3. #92318⋊C2 | C2 | direct (N × H) |
| 6. C2×#6903 | C22 | semidirect |
| 7. #92319 | C22 | semidirect |
| 8. #92318 | C22 | semidirect |
| 12. C2×C3⋊D27 | D3 | semidirect |
| 18. #6903 | C23 | semidirect |
| 28. C2×C3×C27 | C2×D3 | semidirect |
| 29. C3⋊D27 | C2×D3 | semidirect |
| 51. C3×C27 | C22×D3 | semidirect |
| 134. C2 | #92318⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92319 | 2 |
| C2×#92318 | 2 |
| #92318⋊C2 | 2 |
| C2×#4207⋊C2 | 3 |
| C2×D3×D27 | 3 |