Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#888 | C2 | semidirect |
| 3. C2×C3×#107 | C2 | semidirect |
| 5. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4890 | C2 | direct (N × H) |
| 24. #888 | C22 | semidirect |
| 25. C3×#107 | C22 | semidirect |
| 27. Dic3⋊C8 | C22 | semidirect |
| 29. #807 | C22 | semidirect |
| 34. C2×#107 | D3 | semidirect |
| 47. C2×D12 | Q8 | semidirect |
| 83. #107 | C2×D3 | semidirect |
| 108. D12 | C2×Q8 | semidirect |
| 184. C2×C3 | #474 | semidirect |
| 205. C3 | C2×#474 | semidirect |
| 207. C2 | #4890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×#888 | 2 |
| C2×C3×#107 | 2 |
| C2×#821 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#809 | 2 |
| C2×#807 | 2 |
| #4890 | 2 |
| C2×#474 | 3 |