Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 149 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. C3×Q82 | C2 | semidirect |
| 4. #5080 | C2 | semidirect |
| 6. Q8×C3⋊C8 | C2 | semidirect |
| 7. #5020 | C2 | semidirect |
| 25. Q82 | D3 | semidirect |
| 45. #215 | Q8 | direct (N × H) |
| 70. C3×Q8 | SD16 | semidirect |
| 71. C3×Q8 | C2×Q8 | semidirect |
| 83. C3⋊C8 | C2×Q8 | semidirect |
| 118. Q8 | #215 | direct (N × H) |
| 119. Q8 | D3×Q8 | semidirect |
| 146. C3 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q82 | 2 |
| Q8×D12 | 2 |
| #5084 | 2 |
| #5080 | 2 |
| C4×#215 | 2 |
| Q8×C3⋊C8 | 2 |
| #5020 | 2 |
| Q8×SD16 | 3 |