Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#575 | C2 | semidirect |
| 2. C2×C3×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C3×#535 | C2 | semidirect |
| 4. C3×#421 | C2 | semidirect |
| 5. C3×#418 | C2 | semidirect |
| 6. C3×#410 | C2 | semidirect |
| 7. C3×#344 | C2 | semidirect |
| 8. #2008 | C3 | direct (N × H) |
| 32. #575 | C2×C3 | semidirect |
| 33. C2×AGL(1,ℤ/8) | C2×C3 | semidirect |
| 34. #535 | C2×C3 | semidirect |
| 35. #421 | C2×C3 | semidirect |
| 36. #418 | C2×C3 | semidirect |
| 37. #410 | C2×C3 | semidirect |
| 38. #344 | C2×C3 | semidirect |
| 49. C2×C3×Q8 | D4 | semidirect |
| 60. C2×C3×D4 | D4 | semidirect |
| 73. C3×M16 | D4 | semidirect |
| 75. C2×C3×C8 | D4 | semidirect |
| 156. C2×Q8 | C3×D4 | semidirect |
| 167. C2×D4 | C3×D4 | semidirect |
| 180. M16 | C3×D4 | semidirect |
| 182. C2×C8 | C3×D4 | semidirect |
| 277. C3 | #2008 | 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 |
| C2×C3×AGL(1,ℤ/8) | 2 |
| C3×#535 | 2 |
| C3×#421 | 2 |
| C3×#418 | 2 |
| C3×#410 | 2 |
| C3×#344 | 2 |
| #2008 | 3 |