Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×C9⋊D9 |
| commutator, cosocle | C2×#6855 | C22 |
| Frattini, socle | C2×C33 | C2×C3⋊D3 |
| Fitting | C22×#6855 | C2 |
| hypercenter | C22×C3 | C9⋊D9 |
| hypocenter | #6855 | D4 |
| LCS | G ▷ C2×#6855 ▷ #6855 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6855 | C2 | semidirect |
| 2. C2×#92197 | C2 | semidirect |
| 3. #11757320 | C2 | semidirect |
| 11. #6855 | D4 | semidirect |
| 23. C22×C3×C9 | D9 | semidirect |
| 56. C3×C9 | #611 | semidirect |
| 91. C22 | #92197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6855 | 2 |
| C2×#92197 | 2 |
| #11757320 | 2 |
| C3×#6233 | 3 |