Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #5075 | C2 | semidirect |
| 3. C8×Dic6 | C2 | semidirect |
| 4. #4544 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 61. Dic6 | D8 | semidirect |
| 63. C3×C8 | SD16 | semidirect |
| 108. C8 | #214 | semidirect |
| 124. C3 | #1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| #5075 | 2 |
| C8×Dic6 | 2 |
| #4544 | 2 |
| #4458 | 2 |
| #1668 | 3 |