Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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×C3×C4×Q8 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 4. #5027 | C2 | direct (N × H) |
| 5. C2×#809 | C2 | semidirect |
| 6. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 13. C3×C4×Q8 | C22 | semidirect |
| 19. C2×#215 | C22 | semidirect |
| 23. #809 | C22 | semidirect |
| 24. C4⋊(C3⋊C8) | C22 | semidirect |
| 27. C2×C4×Q8 | D3 | semidirect |
| 34. C2×C3×Q8 | D4 | semidirect |
| 68. C4×Q8 | C2×D3 | semidirect |
| 82. C3×Q8 | C2×D4 | semidirect |
| 88. C2×C3×C4 | SD16 | semidirect |
| 104. C2×Q8 | D12 | semidirect |
| 140. C3×C4 | C2×SD16 | semidirect |
| 150. Q8 | C2×D12 | semidirect |
| 161. C2×C4 | #215 | semidirect |
| 169. C2×C3 | #460 | semidirect |
| 186. C4 | C2×#215 | semidirect |
| 189. C3 | C2×#460 | semidirect |
| 191. C2 | #5027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| C22×#215 | 2 |
| C2×#874 | 2 |
| #5027 | 2 |
| C2×#809 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#460 | 3 |