Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
992 conjugacy classes of subgroups; only the 624 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 624 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C33 |
| commutator, Frattini, cosocle | C32 | C23×C33 |
| prime radical | C23×C33 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6894 | C2 | direct (N × H) |
| 4. C23×C9⋊C9 | C3 | semidirect |
| 5. C23×C9⋊C9 | C3 | semidirect |
| 7. C2×#6894 | C22 | direct (N × H) |
| 10. C22×C9⋊C9 | C2×C3 | semidirect |
| 11. C22×C9⋊C9 | C2×C3 | semidirect |
| 13. #6894 | C23 | direct (N × H) |
| 23. C2×C9⋊C9 | C22×C3 | semidirect |
| 24. C2×C9⋊C9 | C22×C3 | semidirect |
| 35. C9⋊C9 | C23×C3 | semidirect |
| 36. C9⋊C9 | C23×C3 | semidirect |
| 45. C23×C9 | 3−1+2 | semidirect |
| 60. C22×C9 | C2×3−1+2 | semidirect |
| 79. C2×C9 | C22×3−1+2 | semidirect |
| 91. C9 | C23×3−1+2 | semidirect |
| 92. C23 | #6894 | direct (N × H) |
| 97. C22 | C2×#6894 | direct (N × H) |
| 102. C2 | C22×#6894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6894 | 2 |
| C23×C3×3−1+2 | 3 |
| C23×C32×C9 | 3 |
| C23×C9⋊C9 | 3 |
| C23×C32⋊C9 | 3 |