Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D3 |
| commutator | C22×C3 | C22×C4 |
| Fitting | C2×C3×C42 | C2 |
| socle, cosocle | C23×C3 | C23 |
| prime radical | C22×D12 | C2 |
| hypercenter | C2×C42 | D3 |
| hypocenter | C3 | #390 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C42 | C2 | semidirect |
| 3. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C4⋊Dic3 | C2 | semidirect |
| 12. C2×D12 | C4 | semidirect |
| 19. C2×C42 | D3 | semidirect |
| 31. C2×C3×C4 | D4 | semidirect |
| 56. C3×C4 | C22⋊C4 | semidirect |
| 71. C2×C4 | D12 | semidirect |
| 91. C4 | (C2×D3)⋊C4 | semidirect |
| 92. C3 | #390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D12 | 2 |
| C2×C3×C42 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C2×C4⋊Dic3 | 2 |
| #390 | 3 |