Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 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 |
| 4. #5079 | C2 | semidirect |
| 6. Q8×C3⋊C8 | C2 | semidirect |
| 7. #5020 | C2 | semidirect |
| 25. #557 | D3 | semidirect |
| 70. C3×Q8 | SD16 | semidirect |
| 117. Q8 | #215 | semidirect |
| 144. C3 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| Q8×D12 | 2 |
| #5083 | 2 |
| #5079 | 2 |
| C4×#215 | 2 |
| Q8×C3⋊C8 | 2 |
| #5020 | 2 |
| #3359 | 3 |