Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5078 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 6. #4482 | C2 | semidirect |
| 7. #4480 | C2 | semidirect |
| 84. C3⋊C8 | SD16 | semidirect |
| 152. C3 | #1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#461 | 2 |
| #5078 | 2 |
| #5019 | 2 |
| #5012 | 2 |
| #4547 | 2 |
| #4482 | 2 |
| #4480 | 2 |
| #1693 | 3 |