Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#939 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#575 | C2 |
| socle | C2×C3 | C2×#121 |
| hypercenter | #575 | D3 |
| hypocenter | C3 | #3068 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#575 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#949 | C2 | semidirect |
| 4. #5819 | C2 | semidirect |
| 5. #5237 | C2 | semidirect |
| 6. #5203 | C2 | semidirect |
| 7. #5199 | C2 | semidirect |
| 8. C2×#823 | C2 | semidirect |
| 9. #5124 | C2 | semidirect |
| 15. C3×#137 | C22 | semidirect |
| 17. C3×AGL(1,ℤ/8) | C22 | semidirect |
| 25. #948 | C22 | semidirect |
| 27. C2×#215 | C22 | semidirect |
| 29. C2×#213 | C22 | semidirect |
| 34. #836 | C22 | semidirect |
| 35. #833 | C22 | semidirect |
| 36. #823 | C22 | semidirect |
| 37. #822 | C22 | semidirect |
| 38. #575 | D3 | semidirect |
| 97. #137 | C2×D3 | semidirect |
| 103. AGL(1,ℤ/8) | C2×D3 | semidirect |
| 287. C3 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#575 | 2 |
| C2×#949 | 2 |
| #5819 | 2 |
| #5237 | 2 |
| #5203 | 2 |
| #5199 | 2 |
| C2×#823 | 2 |
| #5124 | 2 |
| #3068 | 3 |