Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#815 | C2 | semidirect |
| 4. Dic3×C4⋊C4 | C2 | semidirect |
| 6. C3×#340 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 20. #893 | C4 | semidirect |
| 22. #821 | C4 | semidirect |
| 24. #809 | C4 | semidirect |
| 31. #340 | D3 | semidirect |
| 50. C2×C3×C8 | C2×C4 | semidirect |
| 54. C3×C4⋊C4 | C2×C4 | semidirect |
| 57. C4⋊Dic3 | C2×C4 | semidirect |
| 63. C2×C3⋊C8 | C2×C4 | semidirect |
| 112. D12 | C42 | semidirect |
| 137. C2×C8 | C4×D3 | semidirect |
| 143. C4⋊C4 | C4×D3 | semidirect |
| 238. C3 | #1762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×#821 | 2 |
| C2×#815 | 2 |
| Dic3×C4⋊C4 | 2 |
| C2×#809 | 2 |
| C3×#340 | 2 |
| #4529 | 2 |
| #1762 | 3 |