Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D3 |
| commutator, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting, prime radical | C22×C3×D4 | C2 |
| socle | C23×C3 | C23 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | C2×#123 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×Dic3 | C2 | semidirect |
| 3. C2×#217 | C2 | semidirect |
| 4. C2×#217 | C2 | semidirect |
| 5. #935 | C2 | direct (N × H) |
| 6. C2×Dic3⋊C4 | C2 | semidirect |
| 16. C22×Dic3 | C22 | semidirect |
| 17. #217 | C22 | semidirect |
| 18. #217 | C22 | semidirect |
| 19. Dic3⋊C4 | C22 | semidirect |
| 82. C2×C3 | #123 | semidirect |
| 97. C3 | C2×#123 | semidirect |
| 100. C2 | #935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C23×Dic3 | 2 |
| C2×#217 | 2 |
| #935 | 2 |
| C2×Dic3⋊C4 | 2 |
| C2×#123 | 3 |