Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#217 | C2 | semidirect |
| 3. #5798 | C2 | direct (N × H) |
| 4. C2×D4×Dic3 | C2 | semidirect |
| 5. C2×#926 | C2 | semidirect |
| 8. C22×C3×D4 | C4 | semidirect |
| 12. C23×Dic3 | C22 | semidirect |
| 14. C2×#217 | C22 | semidirect |
| 15. C2×#217 | C22 | semidirect |
| 16. D4×Dic3 | C22 | semidirect |
| 17. #926 | C22 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C2×C4×Dic3 | C22 | semidirect |
| 26. C24×C3 | C2×C4 | semidirect |
| 30. C2×C3×D4 | C2×C4 | semidirect |
| 31. C2×C3×D4 | C2×C4 | semidirect |
| 33. C22×C3×C4 | C2×C4 | semidirect |
| 38. C22×Dic3 | C23 | semidirect |
| 40. #217 | C23 | semidirect |
| 41. C4⋊Dic3 | C23 | semidirect |
| 42. C4×Dic3 | C23 | semidirect |
| 44. C22×D4 | Dic3 | semidirect |
| 62. C23×C3 | C22×C4 | semidirect |
| 66. C3×D4 | C22×C4 | semidirect |
| 68. C2×C3×C4 | C22×C4 | semidirect |
| 74. C24 | C2×Dic3 | semidirect |
| 78. C2×D4 | C2×Dic3 | semidirect |
| 79. C2×D4 | C2×Dic3 | semidirect |
| 84. C22×C4 | C2×Dic3 | semidirect |
| 109. C23 | C22×Dic3 | semidirect |
| 113. D4 | C22×Dic3 | semidirect |
| 118. C2×C4 | C22×Dic3 | semidirect |
| 122. C2×C3 | #518 | semidirect |
| 137. C3 | C2×#518 | semidirect |
| 140. C2 | #5798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×#217 | 2 |
| #5798 | 2 |
| C2×D4×Dic3 | 2 |
| C2×#926 | 2 |
| C2×#518 | 3 |