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×#102 | C2 | semidirect |
| 4. C2×#832 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C2×#817 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4777 | C2 | direct (N × H) |
| 24. D3×C4⋊C4 | C22 | semidirect |
| 25. C3×#102 | C22 | semidirect |
| 26. #832 | C22 | semidirect |
| 27. (C2×D3)⋊C8 | C22 | semidirect |
| 28. #817 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 36. C2×#102 | D3 | semidirect |
| 87. #102 | C2×D3 | semidirect |
| 202. C2×C3 | #481 | semidirect |
| 226. C3 | C2×#481 | semidirect |
| 229. C2 | #4777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#938 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#817 | 2 |
| C2×#808 | 2 |
| #4777 | 2 |
| C2×#481 | 3 |