Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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×C3×#137 | C2 | semidirect |
| 3. #5816 | C2 | semidirect |
| 4. #5240 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5139 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 33. C2×#137 | D3 | semidirect |
| 266. C3 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5822 | 2 |
| #5816 | 2 |
| #5240 | 2 |
| #5225 | 2 |
| #5139 | 2 |
| #4559 | 2 |
| #2009 | 3 |