Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D3 |
| commutator, cosocle | C23×C3 | C24 |
| Frattini | C23 | C23×D3 |
| Fitting | C23×C3×Q8 | C2 |
| socle, prime radical | C24×C3 | C23 |
| hypercenter | C23×Q8 | D3 |
| hypocenter | C3 | C2×#395 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #5230 | C2 | direct (N × H) |
| 27. C22×Dic3 | Q8 | semidirect |
| 52. C2×Dic3 | C2×Q8 | semidirect |
| 89. C2×C3 | #395 | semidirect |
| 102. C3 | C2×#395 | semidirect |
| 103. C2 | #5230 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C22×Dic3⋊C4 | 2 |
| #5230 | 2 |
| C2×C3⋊#95 | 2 |
| C2×#395 | 3 |