Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #4960 | C2 |
| hypercenter | #385 | D3 |
| hypocenter | C3 | #2463 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×#67 | C2 | semidirect |
| 2. C2×#896 | C2 | semidirect |
| 3. C3×#385 | C2 | semidirect |
| 4. #4990 | C2 | semidirect |
| 6. #4959 | C2 | semidirect |
| 7. #4947 | C2 | semidirect |
| 8. #4665 | C2 | semidirect |
| 9. #4652 | C2 | semidirect |
| 42. #385 | D3 | semidirect |
| 73. Dic3⋊C4 | D4 | semidirect |
| 259. C3 | #2463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#67 | 2 |
| C2×#896 | 2 |
| C3×#385 | 2 |
| #4990 | 2 |
| #4960 | 2 |
| #4959 | 2 |
| #4947 | 2 |
| #4665 | 2 |
| #4652 | 2 |
| #2463 | 3 |