Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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×#385 | C2 |
| prime radical | C24×C3 | C23 |
| hypercenter | #385 | D3 |
| hypocenter | C3 | #2722 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4984 | C2 | semidirect |
| 5. #4981 | C2 | semidirect |
| 8. #4661 | C2 | semidirect |
| 9. #4653 | C2 | semidirect |
| 212. C3 | #2722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#879 | 2 |
| C3×#385 | 2 |
| #5212 | 2 |
| #4984 | 2 |
| #4981 | 2 |
| #4953 | 2 |
| #4661 | 2 |
| #4653 | 2 |
| #2722 | 3 |