Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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. C8×Dic6 | C2 | semidirect |
| 5. #4484 | C2 | semidirect |
| 6. #4480 | C2 | semidirect |
| 7. #4455 | C2 | semidirect |
| 76. Dic6 | M16 | semidirect |
| 79. C3×C8 | SD16 | semidirect |
| 133. C8 | #214 | semidirect |
| 150. C3 | #1583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#436 | 2 |
| C4×#214 | 2 |
| C8×Dic6 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4484 | 2 |
| #4480 | 2 |
| #4455 | 2 |
| #1583 | 3 |