Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#419 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #419 | D3 |
| hypocenter | C3 | #3010 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #419 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#1007 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. #5525 | C2 | semidirect |
| 5. C3×#419 | C2 | semidirect |
| 6. #5129 | C2 | semidirect |
| 7. #5002 | C2 | semidirect |
| 8. #4810 | C2 | semidirect |
| 9. #4806 | C2 | semidirect |
| 15. C2×#239 | C22 | semidirect |
| 17. C2×D3×Q8 | C22 | semidirect |
| 34. C3×#103 | C22 | semidirect |
| 35. (C2×D3)⋊C8 | C22 | semidirect |
| 36. #810 | C22 | semidirect |
| 37. #809 | C22 | semidirect |
| 44. #419 | D3 | semidirect |
| 50. C2×C3×Q8 | D4 | semidirect |
| 66. #235 | D4 | semidirect |
| 117. #103 | C2×D3 | semidirect |
| 176. C2×Q8 | D12 | semidirect |
| 284. C3 | #3010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| C22×#215 | 2 |
| C2×#908 | 2 |
| #5525 | 2 |
| C3×#419 | 2 |
| #5129 | 2 |
| #5002 | 2 |
| #4810 | 2 |
| #4806 | 2 |
| #3010 | 3 |