Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #4830 | C2 | semidirect |
| 5. #4480 | C2 | semidirect |
| 6. #4456 | C2 | semidirect |
| 7. C8×C3⋊C8 | C2 | semidirect |
| 39. #214 | C8 | semidirect |
| 76. Dic6 | C2×C8 | semidirect |
| 82. C3⋊C8 | C2×C8 | semidirect |
| 83. C3⋊C8 | SD16 | semidirect |
| 150. C3 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#214 | 2 |
| D4×C3⋊C8 | 2 |
| #4830 | 2 |
| C3×D4⋊C8 | 2 |
| #4480 | 2 |
| #4456 | 2 |
| C8×C3⋊C8 | 2 |
| C8×SD16 | 3 |