Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C3×#532 | C2 | semidirect |
| 2. C2×#950 | C2 | semidirect |
| 3. #5477 | C2 | semidirect |
| 4. #5086 | C2 | semidirect |
| 5. #5074 | C2 | semidirect |
| 6. #5060 | C2 | semidirect |
| 7. #5058 | C2 | semidirect |
| 8. C2×#803 | C2 | semidirect |
| 33. #532 | D3 | semidirect |
| 64. C2×C3⋊C8 | D4 | semidirect |
| 189. C3 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C2×#950 | 2 |
| #5477 | 2 |
| #5086 | 2 |
| #5074 | 2 |
| #5060 | 2 |
| #5058 | 2 |
| C2×#803 | 2 |
| #3150 | 3 |