Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
398 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #92172 |
| commutator, cosocle, hypocenter | C3×C27 | C23×C3 |
| Frattini | C3×C9 | C22×C3×D3 |
| Fitting | C22×C32⋊C27 | C2 |
| socle | C22×C32 | 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×C32⋊C27 | C2 | semidirect |
| 2. C2×#92172 | C2 | direct (N × H) |
| 4. C22×C3⋊D27 | C3 | semidirect |
| 5. C2×C32⋊C27 | C22 | semidirect |
| 6. #92172 | C22 | direct (N × H) |
| 10. C22×C3×C27 | C2×C3 | semidirect |
| 11. C2×C3⋊D27 | C2×C3 | semidirect |
| 12. C32⋊C27 | C23 | semidirect |
| 21. C2×C3×C27 | C22×C3 | semidirect |
| 22. C3⋊D27 | C22×C3 | semidirect |
| 37. C3×C27 | C23×C3 | semidirect |
| 59. C22×C32 | D27 | semidirect |
| 84. C2×C32 | C2×D27 | semidirect |
| 107. C32 | C22×D27 | semidirect |
| 123. C22 | #92172 | direct (N × H) |
| 130. C2 | C2×#92172 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32⋊C27 | 2 |
| C2×#92172 | 2 |
| C22×C3×C3⋊D9 | 3 |
| C22×C3⋊D27 | 3 |