Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
464 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C2×C3×C22⋊Q8 | C2 |
| prime radical | C24×C3 | C23 |
| hypercenter | C2×C22⋊Q8 | D3 |
| hypocenter | C3 | #2625 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #5229 | C2 | semidirect |
| 5. #4986 | C2 | semidirect |
| 6. #4981 | C2 | semidirect |
| 7. #4972 | C2 | semidirect |
| 188. C3 | #2625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊Q8 | 2 |
| C2×#926 | 2 |
| #5229 | 2 |
| #5212 | 2 |
| #4986 | 2 |
| #4981 | 2 |
| #4972 | 2 |
| #4952 | 2 |
| #2625 | 3 |