Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 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. C2×C3×#100 | C2 | semidirect |
| 3. #5215 | C2 | semidirect |
| 4. #5139 | C2 | semidirect |
| 5. #5132 | C2 | semidirect |
| 6. #5125 | C2 | semidirect |
| 7. #4556 | C2 | semidirect |
| 31. C2×#100 | D3 | semidirect |
| 214. C3 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#932 | 2 |
| C2×C3×#100 | 2 |
| #5215 | 2 |
| #5139 | 2 |
| #5132 | 2 |
| #5125 | 2 |
| #4556 | 2 |
| #2048 | 3 |