Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
188 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C32 | C32×A4 |
| commutator, cosocle | C32×Q8 | C33 |
| Fitting | Q8×C32⋊C9 | C3 |
| prime radical | C2×C33 | C3×A4 |
| hypercenter | C2×C32⋊C9 | A4 |
| hypocenter | Q8 | #6899 |
| LCS | G ▷ C32×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C9⋊(Q8⋊C9) | C3 | semidirect |
| 6. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 7. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 8. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 9. C9×Q8⋊C9 | C3 | semidirect |
| 120. Q8 | #6899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6204 | 3 |
| Q8×C32⋊C9 | 3 |
| #10619584 | 3 |
| C9⋊(Q8⋊C9) | 3 |
| (Q8⋊C9)⋊C9 | 3 |
| C9×Q8⋊C9 | 3 |
| C2×#6899 | 4 |