Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1184 conjugacy classes of subgroups; only the 496 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 496 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66437 | C2 | direct (N × H) |
| 3. C2×C3×#1094 | C3 | semidirect |
| 4. C2×C32×C22⋊C9 | C3 | semidirect |
| 5. C2×#66437 | C3 | direct (N × H) |
| 10. C3×#1094 | C2×C3 | semidirect |
| 11. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. #66437 | C2×C3 | direct (N × H) |
| 16. C2×#1094 | C32 | semidirect |
| 19. C2×C3×C22⋊C9 | C32 | semidirect |
| 32. #1094 | C2×C32 | semidirect |
| 35. C3×C22⋊C9 | C2×C32 | semidirect |
| 73. C23×C3 | #737 | semidirect |
| 93. C22×C3 | C2×#737 | semidirect |
| 100. C23 | C3×#737 | semidirect |
| 108. C2×C3 | #66437 | direct (N × H) |
| 112. C22 | C2×C3×#737 | semidirect |
| 114. C3 | C2×#66437 | direct (N × H) |
| 118. C2 | C3×#66437 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66437 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×#66437 | 3 |
| C2×C3×#737 | 4 |