Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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. Q8×C3⋊C8 | C2 | semidirect |
| 4. #4535 | C2 | semidirect |
| 6. #4457 | C2 | semidirect |
| 7. C8×C3⋊C8 | C2 | semidirect |
| 34. C3×SD16 | C8 | semidirect |
| 66. C3×Q8 | C2×C8 | semidirect |
| 78. C3×C8 | C2×C8 | semidirect |
| 83. C3⋊C8 | SD16 | direct (N × H) |
| 87. SD16 | C3⋊C8 | direct (N × H) |
| 116. Q8 | C2×C3⋊C8 | semidirect |
| 133. C8 | C2×C3⋊C8 | semidirect |
| 150. C3 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×SD16 | 2 |
| Q8×C3⋊C8 | 2 |
| D4×C3⋊C8 | 2 |
| #4535 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4457 | 2 |
| C8×C3⋊C8 | 2 |
| C8×SD16 | 3 |