Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
568 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 197 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 | C22×C3 | C23×C4 |
| Fitting | C3×#383 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C23×D3 | C23 |
| hypercenter | #383 | D3 |
| hypocenter | C3 | #2283 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#383 | C2 | semidirect |
| 3. #4937 | C2 | semidirect |
| 7. #4650 | C2 | semidirect |
| 8. #4649 | C2 | semidirect |
| 9. #4648 | C2 | semidirect |
| 21. C42×D3 | C4 | semidirect |
| 31. #383 | D3 | semidirect |
| 189. C3 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D3 | 2 |
| C3×#383 | 2 |
| #4937 | 2 |
| #4667 | 2 |
| #4666 | 2 |
| #4664 | 2 |
| #4650 | 2 |
| #4649 | 2 |
| #4648 | 2 |
| #2283 | 3 |