Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×#919 | C2 | semidirect |
| 2. C2×D3×D8 | C2 | semidirect |
| 3. C2×C3×SD32 | C2 | semidirect |
| 4. C2×#828 | C2 | semidirect |
| 5. C2×#826 | C2 | semidirect |
| 6. #4914 | C2 | direct (N × H) |
| 7. C2×D48 | C2 | semidirect |
| 8. C2×#798 | C2 | semidirect |
| 12. C2×C3×Q16 | C22 | semidirect |
| 17. #919 | C22 | semidirect |
| 19. D3×D8 | C22 | semidirect |
| 21. C2×D24 | C22 | semidirect |
| 23. C3×SD32 | C22 | semidirect |
| 24. C2×C3×C16 | C22 | semidirect |
| 25. #828 | C22 | semidirect |
| 26. #826 | C22 | semidirect |
| 27. C2×C3⋊C16 | C22 | semidirect |
| 28. D48 | C22 | semidirect |
| 29. #798 | C22 | semidirect |
| 34. C2×SD32 | D3 | semidirect |
| 52. C3×Q16 | C23 | semidirect |
| 62. D24 | C23 | semidirect |
| 65. C3×C16 | C23 | semidirect |
| 66. C3⋊C16 | C23 | semidirect |
| 71. C2×Q16 | C2×D3 | semidirect |
| 81. SD32 | C2×D3 | semidirect |
| 86. C2×C16 | C2×D3 | semidirect |
| 126. Q16 | C22×D3 | semidirect |
| 140. C16 | C22×D3 | semidirect |
| 181. C2×C3 | #509 | semidirect |
| 200. C3 | C2×#509 | semidirect |
| 205. C2 | #4914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×D3×D8 | 2 |
| C2×C3×SD32 | 2 |
| C2×#828 | 2 |
| C2×#826 | 2 |
| #4914 | 2 |
| C2×D48 | 2 |
| C2×#798 | 2 |
| C2×#509 | 3 |