Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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. #5486 | C2 | semidirect |
| 3. C2×C3×#99 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. C2×#806 | C2 | semidirect |
| 6. D3×#99 | C2 | semidirect |
| 7. #4740 | C2 | semidirect |
| 10. C22×#67 | C4 | semidirect |
| 15. C2×#237 | C4 | semidirect |
| 17. C2×D3×D4 | C4 | semidirect |
| 19. C2×#235 | C4 | semidirect |
| 20. C2×C3×C22⋊C4 | C22 | semidirect |
| 21. C2×#217 | C22 | semidirect |
| 24. D3×C22⋊C4 | C22 | semidirect |
| 25. #877 | C22 | semidirect |
| 26. C3×#99 | C22 | semidirect |
| 27. #834 | C22 | semidirect |
| 28. #806 | C22 | semidirect |
| 35. C2×#99 | D3 | semidirect |
| 36. C24×C3 | C2×C4 | semidirect |
| 38. C23×D3 | C2×C4 | semidirect |
| 39. C23×D3 | C2×C4 | semidirect |
| 43. C2×C3×D4 | C2×C4 | semidirect |
| 46. C22×C3×C4 | C2×C4 | semidirect |
| 53. C2×#67 | C2×C4 | semidirect |
| 54. C2×#67 | C2×C4 | semidirect |
| 55. C2×#67 | C2×C4 | semidirect |
| 60. C22×Dic3 | C2×C4 | semidirect |
| 61. C22×Dic3 | C2×C4 | semidirect |
| 69. C2×D12 | C2×C4 | semidirect |
| 71. C2×C4×D3 | C2×C4 | semidirect |
| 72. C2×C4×D3 | C2×C4 | semidirect |
| 73. C2×Dic6 | C2×C4 | semidirect |
| 97. C2×C22⋊C4 | C2×D3 | semidirect |
| 100. #99 | C2×D3 | semidirect |
| 149. C24 | C4×D3 | semidirect |
| 173. C2×D4 | C4×D3 | semidirect |
| 183. C22×C4 | C4×D3 | semidirect |
| 297. C3 | #2883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| #5486 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| C2×#806 | 2 |
| D3×#99 | 2 |
| #4740 | 2 |
| #2883 | 3 |