Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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×#951 | C2 | semidirect |
| 3. #5526 | C2 | semidirect |
| 4. C3×#410 | C2 | semidirect |
| 5. #5005 | C2 | semidirect |
| 6. #5004 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 37. #410 | 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×#951 | 2 |
| #5822 | 2 |
| #5526 | 2 |
| C3×#410 | 2 |
| #5005 | 2 |
| #5004 | 2 |
| #4533 | 2 |
| #2009 | 3 |