Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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. #5092 | C2 | semidirect |
| 5. #5085 | C2 | semidirect |
| 6. #5076 | C2 | semidirect |
| 7. #5073 | C2 | semidirect |
| 8. #5059 | C2 | semidirect |
| 9. C2×C4×C3⋊C8 | C2 | semidirect |
| 35. #532 | D3 | semidirect |
| 67. C2×C3⋊C8 | D4 | semidirect |
| 153. C3×C4 | #135 | semidirect |
| 195. C4 | #950 | semidirect |
| 197. C3 | #3147 | 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 |
| #5092 | 2 |
| #5085 | 2 |
| #5076 | 2 |
| #5073 | 2 |
| #5059 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #3147 | 3 |