Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3 |
| socle | C2×C3 | #394 |
| prime radical | C3×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#423 | C2 | semidirect |
| 3. C2×C3×#104 | C2 | semidirect |
| 4. C3×#413 | C2 | semidirect |
| 5. C3×#338 | C2 | semidirect |
| 6. #2050 | C3 | direct (N × H) |
| 21. #423 | C2×C3 | semidirect |
| 22. C2×#104 | C2×C3 | semidirect |
| 23. #413 | C2×C3 | semidirect |
| 24. #338 | C2×C3 | semidirect |
| 152. C3 | #2050 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#575 | 2 |
| C3×#423 | 2 |
| C2×C3×#104 | 2 |
| C3×#413 | 2 |
| C3×#338 | 2 |
| #2050 | 3 |