Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C3 | C22×C42 |
| Fitting | C2×C3×#95 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×#67 | C22 |
| hypercenter | C2×#95 | D3 |
| hypocenter | C3 | #2275 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#95 | C2 | semidirect |
| 3. C4×#217 | C2 | semidirect |
| 4. #4666 | C2 | semidirect |
| 5. D3×#95 | C2 | semidirect |
| 6. #4649 | C2 | semidirect |
| 7. #4648 | C2 | semidirect |
| 13. C4×#67 | C4 | semidirect |
| 28. C2×#95 | D3 | semidirect |
| 32. C22×C3×C4 | C2×C4 | semidirect |
| 40. C2×C4×D3 | C2×C4 | semidirect |
| 41. #217 | C2×C4 | semidirect |
| 42. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 43. Dic3⋊C4 | C2×C4 | semidirect |
| 45. C4×Dic3 | C2×C4 | semidirect |
| 71. #67 | C42 | semidirect |
| 88. C22×C4 | C4×D3 | semidirect |
| 149. C3 | #2275 | 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×C3×#95 | 2 |
| C4×#217 | 2 |
| #4666 | 2 |
| D3×#95 | 2 |
| #4649 | 2 |
| #4648 | 2 |
| #2275 | 3 |