Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. C3×#413 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. #4478 | C2 | semidirect |
| 5. #4477 | C2 | semidirect |
| 26. #413 | D3 | semidirect |
| 216. C3 | #2132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5832 | 2 |
| C3×#413 | 2 |
| #5237 | 2 |
| #4478 | 2 |
| #4477 | 2 |
| #2132 | 3 |