Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 213 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×C43 | C2 |
| prime radical | C2×#874 | C2 |
| hypercenter | C43 | D3 |
| hypocenter | C3 | #2858 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#875 | C2 | semidirect |
| 3. C2×#869 | C2 | semidirect |
| 4. C3×C43 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 22. C43 | D3 | semidirect |
| 36. C3×C42 | D4 | semidirect |
| 80. C42 | D12 | semidirect |
| 88. C3×C4 | #124 | semidirect |
| 119. C4 | #875 | semidirect |
| 120. C3 | #2858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C2×#874 | 2 |
| C2×#869 | 2 |
| C3×C43 | 2 |
| #4939 | 2 |
| #2858 | 3 |