Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 139 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×#557 | C2 | semidirect |
| 3. #5085 | C2 | semidirect |
| 4. #5083 | C2 | semidirect |
| 5. #5027 | C2 | semidirect |
| 6. C4×#215 | C2 | semidirect |
| 7. Q8×C3⋊C8 | C2 | semidirect |
| 25. #557 | D3 | semidirect |
| 71. C3×Q8 | SD16 | semidirect |
| 84. C3⋊C8 | #41 | semidirect |
| 119. Q8 | #215 | semidirect |
| 148. C3 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5577 | 2 |
| #5085 | 2 |
| #5083 | 2 |
| #5027 | 2 |
| C4×#215 | 2 |
| Q8×C3⋊C8 | 2 |
| #3392 | 3 |