Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C2×C3×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#108 | C2 | semidirect |
| 3. C3×#417 | C2 | semidirect |
| 4. C2×C3×#102 | C2 | semidirect |
| 5. C2×C3×#100 | C2 | semidirect |
| 6. C3×#408 | C2 | semidirect |
| 7. C3×#343 | C2 | semidirect |
| 8. #2051 | C3 | direct (N × H) |
| 27. C2×#108 | C2×C3 | semidirect |
| 28. #417 | C2×C3 | semidirect |
| 29. C2×#102 | C2×C3 | semidirect |
| 30. C2×#100 | C2×C3 | semidirect |
| 31. #408 | C2×C3 | semidirect |
| 32. #343 | C2×C3 | semidirect |
| 225. C3 | #2051 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| C2×C3×#108 | 2 |
| C3×#417 | 2 |
| C2×C3×#102 | 2 |
| C2×C3×#100 | 2 |
| C3×#408 | 2 |
| C3×#343 | 2 |
| #2051 | 3 |