Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #5477 | C2 | semidirect |
| 3. #5088 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 5. #5073 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. #5038 | C2 | semidirect |
| 8. C4×#213 | C2 | semidirect |
| 9. C2×C4×C3⋊C8 | C2 | semidirect |
| 37. #532 | D3 | semidirect |
| 115. C2×C3×C4 | D8 | semidirect |
| 130. C3⋊C8 | #41 | semidirect |
| 201. C2×C4 | #213 | semidirect |
| 234. C3 | #3169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5477 | 2 |
| #5088 | 2 |
| #5078 | 2 |
| #5073 | 2 |
| #5070 | 2 |
| #5038 | 2 |
| C4×#213 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #3169 | 3 |