Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C23 |
| commutator | C22 | C22×C3×C4 |
| Frattini, cosocle | C23 | C23×C3 |
| prime radical | C22×C3×D4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×C22⋊C4 | C2 | semidirect |
| 4. C2×C3×C42 | C2 | semidirect |
| 5. #390 | C3 | direct (N × H) |
| 9. C2×C3×D4 | C4 | semidirect |
| 17. C2×C4⋊C4 | C2×C3 | semidirect |
| 18. C2×C22⋊C4 | C2×C3 | semidirect |
| 19. C2×C42 | C2×C3 | semidirect |
| 34. C2×C3×C4 | D4 | semidirect |
| 38. C2×D4 | C3×C4 | semidirect |
| 57. C3×C4 | C22⋊C4 | semidirect |
| 72. C2×C4 | C3×D4 | semidirect |
| 91. C4 | C3×C22⋊C4 | semidirect |
| 92. C3 | #390 | 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 |
| C2×C3×C4⋊C4 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×C3×C42 | 2 |
| #390 | 3 |