Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C3×C4⋊C4 | C2 | semidirect |
| 3. C22×#208 | C2 | semidirect |
| 4. C2×#810 | C2 | semidirect |
| 5. #4966 | C2 | direct (N × H) |
| 6. C2×#809 | C2 | semidirect |
| 13. C2×#235 | C4 | semidirect |
| 21. C2×C3×C4⋊C4 | C22 | semidirect |
| 23. C2×#208 | C22 | semidirect |
| 25. #810 | C22 | semidirect |
| 26. #809 | C22 | semidirect |
| 29. C22×C4⋊C4 | D3 | semidirect |
| 49. #235 | C2×C4 | semidirect |
| 52. C2×D12 | C2×C4 | semidirect |
| 58. C2×Dic6 | C2×C4 | semidirect |
| 82. C2×C4⋊C4 | C2×D3 | semidirect |
| 111. D12 | C22×C4 | semidirect |
| 115. Dic6 | C22×C4 | semidirect |
| 201. C2×C3 | #417 | semidirect |
| 224. C3 | C2×#417 | semidirect |
| 227. C2 | #4966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×#208 | 2 |
| C2×#810 | 2 |
| #4966 | 2 |
| C2×#809 | 2 |
| C2×#417 | 3 |