Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
217 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | A4×H(3,𝔽3) |
| commutator, cosocle | C32×Q8 | C33 |
| Frattini | C2×C32 | C32×A4 |
| Fitting | Q8×#732 | C3 |
| hypercenter | C2×#732 | A4 |
| hypocenter | Q8 | #6908 |
| LCS | G ▷ C32×Q8 ▷ C3×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C32 ◁ C2×#732 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619913 | C3 | semidirect |
| 2. C3×C9×SL(2,𝔽3) | C3 | semidirect |
| 3. Q8×#732 | C3 | semidirect |
| 4. #10619580 | C3 | semidirect |
| 5. #10619578 | C3 | semidirect |
| 6. #10619576 | C3 | semidirect |
| 31. #732 | SL(2,𝔽3) | semidirect |
| 91. Q8 | #6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619913 | 3 |
| C3×C9×SL(2,𝔽3) | 3 |
| Q8×#732 | 3 |
| #10619580 | 3 |
| #10619578 | 3 |
| #10619576 | 3 |
| C2×#6908 | 4 |