Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C23 |
| Fitting | C32×C22⋊C4 | C2 |
| prime radical | C2×#638 | C2 |
| hypercenter | C22⋊C4 | C3⋊D3 |
| hypocenter | C32 | #124 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#634 | C2 | semidirect |
| 3. C32×C22⋊C4 | C2 | semidirect |
| 4. #3757 | C2 | semidirect |
| 5. #3752 | C2 | semidirect |
| 6. #3752 | C2 | semidirect |
| 7. C4×C3⋊Dic3 | C2 | semidirect |
| 20. C3×C22⋊C4 | D3 | semidirect |
| 57. C22⋊C4 | C3⋊D3 | semidirect |
| 71. C32 | #124 | semidirect |
| 98. C3 | #885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#638 | 2 |
| C2×#634 | 2 |
| C32×C22⋊C4 | 2 |
| #3757 | 2 |
| #3752 | 2 |
| C4×C3⋊Dic3 | 2 |
| #885 | 3 |