Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 223 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×#395 | C2 |
| prime radical | C23×D3 | C23 |
| hypercenter | #395 | D3 |
| hypocenter | C3 | C2×#395 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#395 | C2 | semidirect |
| 4. #5230 | C2 | semidirect |
| 5. #4979 | C2 | semidirect |
| 7. #4656 | C2 | semidirect |
| 28. #395 | D3 | direct (N × H) |
| 44. C2×C4×D3 | Q8 | semidirect |
| 75. C2×C3×C4 | C2×Q8 | semidirect |
| 81. C2×Dic3 | C2×Q8 | semidirect |
| 139. C2×C4 | D3×Q8 | semidirect |
| 143. D3 | #395 | direct (N × H) |
| 156. C3 | C2×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C3×#395 | 2 |
| #5230 | 2 |
| #4979 | 2 |
| D3×#95 | 2 |
| #4656 | 2 |
| C2×#395 | 3 |