Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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 |
|---|---|---|
| 3. C3×#340 | C2 | semidirect |
| 4. #4551 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 15. C2×D3×C8 | C4 | semidirect |
| 17. D3×C4⋊C4 | C4 | semidirect |
| 22. #340 | D3 | direct (N × H) |
| 36. C2×C3×C8 | C2×C4 | semidirect |
| 38. C3×C4⋊C4 | C2×C4 | semidirect |
| 40. C4⋊Dic3 | C2×C4 | semidirect |
| 43. C2×C3⋊C8 | C2×C4 | semidirect |
| 96. C2×C8 | C4×D3 | semidirect |
| 101. C4⋊C4 | C4×D3 | semidirect |
| 147. D3 | #340 | direct (N × H) |
| 164. C3 | C2×#340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C3×#340 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| C2×#340 | 3 |