Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. C2×C4×Dic6 | C2 | semidirect |
| 5. #5210 | C2 | semidirect |
| 6. #4975 | C2 | semidirect |
| 7. #4973 | C2 | semidirect |
| 8. #4944 | C2 | semidirect |
| 9. #4932 | C2 | semidirect |
| 20. #936 | C4 | semidirect |
| 56. C2×Dic6 | C2×C4 | semidirect |
| 61. #217 | C2×C4 | semidirect |
| 67. C4×Dic3 | C2×C4 | 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×C4×D4 | 2 |
| C2×#936 | 2 |
| C2×C4×Dic6 | 2 |
| #5221 | 2 |
| #5210 | 2 |
| #4975 | 2 |
| #4973 | 2 |
| #4944 | 2 |
| #4932 | 2 |
| #2326 | 3 |