Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D3 |
| commutator | C22×C3 | C23×C4 |
| Frattini | C23 | C23×D3 |
| Fitting | C3×C43 | C2 |
| socle, prime radical, cosocle | C23×C3 | C24 |
| hypercenter | C43 | D3 |
| hypocenter | C3 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. #869 | C4 | direct (N × H) |
| 44. C3×C42 | Q8 | semidirect |
| 101. C42 | Dic6 | semidirect |
| 112. C3×C4 | C4×Q8 | semidirect |
| 113. C3×C4 | C4⋊Q8 | semidirect |
| 150. C4 | C4×Dic6 | semidirect |
| 151. C4 | #869 | direct (N × H) |
| 153. C3 | C4×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×C4×Dic6 | 2 |
| C3×C43 | 2 |
| #4935 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4929 | 2 |
| #4928 | 2 |
| C4×C4⋊Q8 | 3 |