Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #11757753 |
| commutator, cosocle, hypocenter | C32×C27 | C23 |
| Frattini | C9 | C2×#1113 |
| Fitting | C2×C32×C27 | C22 |
| socle | C2×C33 | C2×D9 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3⋊D3×C27 | C2 | semidirect |
| 2. C2×C3×C3⋊D27 | C2 | semidirect |
| 3. #11757753 | C2 | direct (N × H) |
| 6. C2×C32×C27 | C22 | semidirect |
| 7. C3⋊D3×C27 | C22 | semidirect |
| 8. C3×C3⋊D27 | C22 | semidirect |
| 12. C2×C3⋊D27 | D3 | semidirect |
| 18. C32×C27 | C23 | semidirect |
| 28. C2×C3×C27 | C2×D3 | semidirect |
| 29. C3⋊D27 | C2×D3 | semidirect |
| 51. C3×C27 | C22×D3 | semidirect |
| 70. C2×C27 | D32 | semidirect |
| 74. C2×C3⋊D3 | D27 | semidirect |
| 93. C27 | C2×D32 | semidirect |
| 99. C2×C32 | C2×D27 | semidirect |
| 102. C3⋊D3 | C2×D27 | semidirect |
| 126. C32 | C22×D27 | semidirect |
| 137. C2×C3 | D3×D27 | semidirect |
| 150. C3 | C2×D3×D27 | semidirect |
| 154. C2 | #11757753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊D3×C27 | 2 |
| C2×C3×C3⋊D27 | 2 |
| #11757753 | 2 |
| C2×#66431 | 3 |
| C2×D3×D27 | 3 |