Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#380 | C2 |
| hypercenter | #380 | D3 |
| hypocenter | C3 | #2617 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#930 | C2 | semidirect |
| 2. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 3. C2×#882 | C2 | semidirect |
| 4. C3×#380 | C2 | semidirect |
| 5. #4991 | C2 | semidirect |
| 6. #4958 | C2 | semidirect |
| 7. #4674 | C2 | semidirect |
| 8. #4671 | C2 | semidirect |
| 15. C22×D12 | C22 | semidirect |
| 16. C2×C3×C4⋊C4 | C22 | semidirect |
| 23. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 25. C2×C4⋊Dic3 | C22 | semidirect |
| 27. C3×#95 | C22 | semidirect |
| 28. C3⋊#95 | C22 | semidirect |
| 36. #380 | D3 | semidirect |
| 42. C23×D3 | D4 | semidirect |
| 46. C22×C3×C4 | D4 | semidirect |
| 79. C2×C4⋊C4 | C2×D3 | semidirect |
| 88. #95 | C2×D3 | semidirect |
| 148. C22×C4 | D12 | semidirect |
| 258. C3 | #2617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C2×#882 | 2 |
| C3×#380 | 2 |
| #4991 | 2 |
| #4958 | 2 |
| #4674 | 2 |
| #4671 | 2 |
| #2617 | 3 |