Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92318 |
| commutator, cosocle, hypocenter | C3×C27 | C23×C3 |
| Frattini | C9 | C22×C3×C3⋊D3 |
| Fitting | C22×#6903 | C2 |
| socle | C22×C3 | C3×C3⋊D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6903 | C2 | semidirect |
| 2. C2×#92318 | C2 | direct (N × H) |
| 4. C22×C3⋊D27 | C3 | semidirect |
| 7. C2×#6903 | C22 | semidirect |
| 8. #92318 | C22 | direct (N × H) |
| 13. C22×C27⋊C3 | D3 | semidirect |
| 15. C22×C3×C27 | D3 | semidirect |
| 16. C22×C3×C27 | C2×C3 | semidirect |
| 17. C2×C3⋊D27 | C2×C3 | semidirect |
| 20. #6903 | C23 | semidirect |
| 31. C2×C27⋊C3 | C2×D3 | semidirect |
| 33. C2×C3×C27 | C2×D3 | semidirect |
| 34. C2×C3×C27 | C22×C3 | semidirect |
| 35. C3⋊D27 | C22×C3 | semidirect |
| 58. C27⋊C3 | C22×D3 | semidirect |
| 60. C3×C27 | C22×D3 | semidirect |
| 61. C3×C27 | C23×C3 | semidirect |
| 142. C22 | #92318 | direct (N × H) |
| 148. C2 | C2×#92318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6903 | 2 |
| C2×#92318 | 2 |
| C22×#4207 | 3 |
| C22×C3⋊D27 | 3 |
| C22×D27⋊C3 | 3 |
| C22×C3×D27 | 3 |