Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×#380 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C24×D3 | C22 |
| hypercenter | #380 | D3 |
| hypocenter | C3 | #2312 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#380 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. #4990 | C2 | semidirect |
| 6. Dic3×C22⋊C4 | C2 | semidirect |
| 7. #4670 | C2 | semidirect |
| 12. C2×C3×C4⋊C4 | C22 | semidirect |
| 15. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 20. C2×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C4×Dic3 | C22 | semidirect |
| 22. C3×#95 | C22 | semidirect |
| 23. C3⋊#95 | C22 | semidirect |
| 24. C3⋊#95 | C22 | semidirect |
| 29. #380 | D3 | semidirect |
| 61. C2×C4⋊C4 | C2×D3 | semidirect |
| 72. #95 | C2×D3 | semidirect |
| 207. C3 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D3)⋊C4 | 2 |
| C3×#380 | 2 |
| #5212 | 2 |
| #4990 | 2 |
| #4955 | 2 |
| Dic3×C22⋊C4 | 2 |
| #4670 | 2 |
| #2312 | 3 |