Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×#924 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×C3×C22⋊C8 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. #4731 | C2 | direct (N × H) |
| 15. C22×Dic6 | C22 | semidirect |
| 16. C22×C3×C8 | C22 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 20. #924 | C22 | semidirect |
| 23. C2×#204 | C22 | semidirect |
| 24. C3×C22⋊C8 | C22 | semidirect |
| 25. #821 | C22 | semidirect |
| 31. C2×C22⋊C8 | D3 | semidirect |
| 55. C2×Dic6 | C23 | semidirect |
| 57. C2×C3×C8 | C23 | semidirect |
| 60. C4⋊Dic3 | C23 | semidirect |
| 73. C22×C8 | C2×D3 | semidirect |
| 80. C22⋊C8 | C2×D3 | semidirect |
| 83. C23×C3 | SD16 | semidirect |
| 138. C2×C8 | C22×D3 | semidirect |
| 148. C22×C3 | C2×SD16 | semidirect |
| 171. C23 | #204 | semidirect |
| 193. C2×C3 | #450 | semidirect |
| 208. C22 | C2×#204 | semidirect |
| 216. C3 | C2×#450 | semidirect |
| 219. C2 | #4731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C2×#924 | 2 |
| C22×#204 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| #4731 | 2 |
| C2×#450 | 3 |