Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D4 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#466 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #466 | D3 |
| hypocenter | C3 | #3285 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #466 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#912 | C2 | semidirect |
| 2. C22×Dic12 | C2 | semidirect |
| 3. #5598 | C2 | semidirect |
| 4. C3×#466 | C2 | semidirect |
| 5. #5155 | C2 | semidirect |
| 6. C8×#67 | C2 | semidirect |
| 7. #5040 | C2 | semidirect |
| 8. #4887 | C2 | semidirect |
| 9. #4873 | C2 | semidirect |
| 10. #4783 | C2 | semidirect |
| 11. #4767 | C2 | semidirect |
| 47. #466 | D3 | semidirect |
| 90. Dic12 | D4 | semidirect |
| 196. C22×C3 | #135 | semidirect |
| 255. C22 | #912 | semidirect |
| 266. C3 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#912 | 2 |
| C22×Dic12 | 2 |
| #5598 | 2 |
| C3×#466 | 2 |
| #5155 | 2 |
| C8×#67 | 2 |
| #5040 | 2 |
| #4887 | 2 |
| #4873 | 2 |
| #4783 | 2 |
| #4767 | 2 |
| #3285 | 3 |