Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. C2×#870 | C2 | semidirect |
| 4. C3×#336 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 20. #336 | D3 | semidirect |
| 144. C3 | #2025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#870 | 2 |
| C2×#821 | 2 |
| #4939 | 2 |
| C3×#336 | 2 |
| #4551 | 2 |
| #2025 | 3 |