Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
| hypercenter | C22⋊C4 | C3⋊D3 |
| hypocenter | C32 | #121 |
| 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 |
|---|---|---|
| 1. C2×#638 | C2 | semidirect |
| 2. C2×#638 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C2×C4×C3⋊D3 | C2 | semidirect |
| 5. C32×C22⋊C4 | C2 | semidirect |
| 6. #3752 | C2 | semidirect |
| 7. #3750 | C2 | semidirect |
| 24. C3×C22⋊C4 | D3 | semidirect |
| 36. C2×C3⋊D3 | D4 | semidirect |
| 40. C3⋊Dic3 | D4 | semidirect |
| 65. C22⋊C4 | C3⋊D3 | semidirect |
| 80. C32 | #121 | semidirect |
| 112. C3 | #884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#638 | 2 |
| C2×C4⋊(C3⋊D3) | 2 |
| C2×C4×C3⋊D3 | 2 |
| C32×C22⋊C4 | 2 |
| #3752 | 2 |
| #3750 | 2 |
| #884 | 3 |