Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
6520 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C23×C3×C4 | C22 |
| commutator, Frattini, cosocle | C2 | C26×C3 |
| socle | C24×C3 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×#41 | C2 | direct (N × H) |
| 2. C23×C3×Q8 | C2 | semidirect |
| 3. C23×C3×D4 | C2 | semidirect |
| 4. C24×C3×C4 | C2 | semidirect |
| 5. C23×#41 | C3 | direct (N × H) |
| 7. C2×C3×#41 | C22 | direct (N × H) |
| 8. C22×C3×Q8 | C22 | semidirect |
| 9. C22×C3×D4 | C22 | semidirect |
| 12. C23×C3×C4 | C22 | semidirect |
| 13. C22×#41 | C2×C3 | direct (N × H) |
| 14. C23×Q8 | C2×C3 | semidirect |
| 15. C23×D4 | C2×C3 | semidirect |
| 16. C24×C4 | C2×C3 | semidirect |
| 20. C3×#41 | C23 | direct (N × H) |
| 21. C2×C3×Q8 | C23 | semidirect |
| 22. C2×C3×D4 | C23 | semidirect |
| 25. C22×C3×C4 | C23 | semidirect |
| 27. C2×#41 | C22×C3 | direct (N × H) |
| 28. C22×Q8 | C22×C3 | semidirect |
| 29. C22×D4 | C22×C3 | semidirect |
| 32. C23×C4 | C22×C3 | semidirect |
| 34. C23×C3 | #41 | direct (N × H) |
| 37. C3×Q8 | C24 | semidirect |
| 38. C3×D4 | C24 | semidirect |
| 41. C2×C3×C4 | C24 | semidirect |
| 45. #41 | C23×C3 | direct (N × H) |
| 46. C2×Q8 | C23×C3 | semidirect |
| 47. C2×D4 | C23×C3 | semidirect |
| 50. C22×C4 | C23×C3 | semidirect |
| 52. C22×C3 | C2×#41 | direct (N × H) |
| 58. C23 | C3×#41 | direct (N × H) |
| 61. Q8 | C24×C3 | semidirect |
| 62. D4 | C24×C3 | semidirect |
| 65. C2×C4 | C24×C3 | semidirect |
| 67. C2×C3 | C22×#41 | direct (N × H) |
| 70. C22 | C2×C3×#41 | direct (N × H) |
| 75. C3 | C23×#41 | direct (N × H) |
| 77. C2 | C22×C3×#41 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C23×C3×Q8 | 2 |
| C23×C3×D4 | 2 |
| C24×C3×C4 | 2 |
| C23×#41 | 3 |