Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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×#500 | C2 | semidirect |
| 4. #4547 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 18. #500 | D3 | semidirect |
| 61. C3×C8 | SD16 | semidirect |
| 104. C8 | #215 | semidirect |
| 120. C3 | #1673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#500 | 2 |
| #5083 | 2 |
| C8×D12 | 2 |
| #4547 | 2 |
| #4458 | 2 |
| #1673 | 3 |