Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
182 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#92214 |
| commutator, cosocle | C2×#6873 | C22 |
| Frattini | C2×C3×C9 | C2×C3⋊D3 |
| Fitting | C4×#6873 | C2 |
| socle | C2×C3 | C2×#4181 |
| hypercenter | C4 | #92214 |
| hypocenter | #6873 | D4 |
| LCS | G ▷ C2×#6873 ▷ #6873 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92214 | C2 | semidirect |
| 2. C4×#6873 | C2 | semidirect |
| 12. C4×C27⋊C3 | D3 | semidirect |
| 13. C3×C4×C27 | D3 | semidirect |
| 14. #6873 | D4 | semidirect |
| 41. C27⋊C3 | D12 | semidirect |
| 42. C3×C27 | D12 | semidirect |
| 107. C4 | #92214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92214 | 2 |
| C4×#6873 | 2 |
| C4⋊#4207 | 3 |
| C4⋊(D27⋊C3) | 3 |
| C3×D108 | 3 |