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. #5521 | C2 | semidirect |
| 3. C3×#410 | C2 | semidirect |
| 4. #5240 | C2 | semidirect |
| 5. #5006 | C2 | semidirect |
| 6. D3×#99 | C2 | semidirect |
| 11. C2×#239 | C4 | semidirect |
| 12. C2×D3×D4 | C4 | semidirect |
| 14. C2×#235 | C4 | semidirect |
| 16. C22×D12 | C4 | semidirect |
| 18. C3×#117 | C22 | semidirect |
| 19. #926 | C22 | semidirect |
| 21. D3×C22⋊C4 | C22 | semidirect |
| 23. C3×#99 | C22 | semidirect |
| 24. #834 | C22 | semidirect |
| 25. #806 | C22 | semidirect |
| 30. #410 | D3 | semidirect |
| 32. C23×D3 | C2×C4 | semidirect |
| 36. C2×C3×Q8 | C2×C4 | semidirect |
| 37. C2×C3×D4 | C2×C4 | semidirect |
| 39. C22×C3×C4 | C2×C4 | semidirect |
| 41. C2×#67 | C2×C4 | semidirect |
| 54. C2×D12 | C2×C4 | semidirect |
| 55. C2×D12 | C2×C4 | semidirect |
| 59. C2×C4×D3 | C2×C4 | semidirect |
| 60. C2×C4×D3 | C2×C4 | semidirect |
| 61. C2×Dic6 | C2×C4 | semidirect |
| 82. #117 | C2×D3 | semidirect |
| 86. #99 | C2×D3 | semidirect |
| 131. C2×Q8 | C4×D3 | semidirect |
| 144. C2×D4 | C4×D3 | semidirect |
| 149. C22×C4 | C4×D3 | semidirect |
| 234. C3 | #2883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| #5521 | 2 |
| C3×#410 | 2 |
| #5240 | 2 |
| #5006 | 2 |
| D3×#99 | 2 |
| #2883 | 3 |