Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
111 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 111 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D32 |
| commutator | C2×C32 | C2×C8 |
| Fitting, cosocle | C2×C32×C4 | C22 |
| socle | C22×C32 | C2×C4 |
| prime radical | C22×C3×D3 | C4 |
| hypocenter | C32 | C22⋊C8 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C2×C3×C3⋊C8 | C2 | semidirect |
| 19. C2×C3⋊C8 | D3 | semidirect |
| 23. C2×C3×D3 | C8 | semidirect |
| 59. C2×D3 | C3⋊C8 | semidirect |
| 68. C32 | C22⋊C8 | semidirect |
| 95. C3 | (C2×D3)⋊C8 | semidirect |
| 96. C3 | #830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D3 | 2 |
| C2×C3⋊(C3⋊C8) | 2 |
| C2×C3×C3⋊C8 | 2 |
| #830 | 3 |
| (C2×D3)⋊C8 | 3 |