Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C2×D3×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×#106 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C2×#809 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4863 | C2 | direct (N × H) |
| 24. D3×C4⋊C4 | C22 | semidirect |
| 25. C3×#106 | C22 | semidirect |
| 26. #821 | C22 | semidirect |
| 27. (C2×D3)⋊C8 | C22 | semidirect |
| 28. #809 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 34. C2×#106 | D3 | semidirect |
| 85. #106 | C2×D3 | semidirect |
| 201. C2×C3 | #481 | semidirect |
| 226. C3 | C2×#481 | semidirect |
| 229. C2 | #4863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#895 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#106 | 2 |
| C2×#821 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| #4863 | 2 |
| C2×#481 | 3 |