Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C2×C3×#123 | C2 |
| prime radical | C2×#937 | C2 |
| hypercenter | C2×#123 | D3 |
| hypocenter | C3 | #2849 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D3 | C2 | semidirect |
| 2. C2×C3×#123 | C2 | semidirect |
| 4. C2×#935 | C2 | semidirect |
| 5. #5211 | C2 | semidirect |
| 6. #4989 | C2 | semidirect |
| 7. #4956 | C2 | semidirect |
| 8. #4955 | C2 | semidirect |
| 9. #4943 | C2 | semidirect |
| 21. C2×C3×C4⋊C4 | C22 | semidirect |
| 23. C2×C3×C22⋊C4 | C22 | semidirect |
| 26. C2×#217 | C22 | semidirect |
| 31. C2×Dic3⋊C4 | C22 | semidirect |
| 32. C3⋊#95 | C22 | semidirect |
| 33. C3⋊#95 | C22 | semidirect |
| 36. C2×#123 | D3 | semidirect |
| 55. C22×C3×C4 | D4 | semidirect |
| 63. C22×Dic3 | D4 | semidirect |
| 93. C2×C4⋊C4 | C2×D3 | semidirect |
| 100. C2×C22⋊C4 | C2×D3 | semidirect |
| 165. C22×C4 | #67 | semidirect |
| 195. C2×D3 | #123 | semidirect |
| 271. C3 | #2849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C2×C3×#123 | 2 |
| C2×#937 | 2 |
| C2×#935 | 2 |
| #5211 | 2 |
| #4989 | 2 |
| #4956 | 2 |
| #4955 | 2 |
| #4943 | 2 |
| #2849 | 3 |