Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D3 |
| commutator, socle, cosocle | C22×C3 | C25 |
| Fitting | C3×C4×#41 | C2 |
| prime radical | C2×C3×#41 | C22 |
| hypercenter | C4×#41 | D3 |
| hypocenter | C3 | #3504 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #5569 | C2 | semidirect |
| 4. #5539 | C2 | semidirect |
| 5. #5519 | C2 | semidirect |
| 6. #5470 | C2 | semidirect |
| 7. C2×#870 | C2 | semidirect |
| 36. C3×#41 | Q8 | semidirect |
| 90. #41 | Dic6 | semidirect |
| 145. C3 | #3504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| #5827 | 2 |
| #5569 | 2 |
| #5539 | 2 |
| #5519 | 2 |
| #5470 | 2 |
| C2×#870 | 2 |
| #3504 | 3 |