Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic3 | C2 | semidirect |
| 4. #5229 | C2 | semidirect |
| 6. #4951 | C2 | semidirect |
| 7. #4950 | C2 | semidirect |
| 8. #4935 | C2 | semidirect |
| 9. #4932 | C2 | semidirect |
| 14. C3×#124 | C4 | semidirect |
| 43. C2×C3×Q8 | C2×C4 | semidirect |
| 57. C3×C22⋊C4 | C2×C4 | semidirect |
| 58. C3×C42 | C2×C4 | semidirect |
| 71. #124 | Dic3 | semidirect |
| 120. C2×Q8 | C2×Dic3 | semidirect |
| 140. C22⋊C4 | C2×Dic3 | semidirect |
| 144. C42 | C2×Dic3 | semidirect |
| 216. C3 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| C2×Q8×Dic3 | 2 |
| C2×D4×Dic3 | 2 |
| #5229 | 2 |
| #5221 | 2 |
| #4951 | 2 |
| #4950 | 2 |
| #4935 | 2 |
| #4932 | 2 |
| #2326 | 3 |