Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #4679 | C2 | semidirect |
| 4. C3×C82 | C2 | semidirect |
| 6. #4457 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 30. C82 | D3 | semidirect |
| 80. C3×C8 | M16 | semidirect |
| 81. C3×C8 | SD16 | semidirect |
| 132. C8 | ΓL(1,𝔽25) | semidirect |
| 133. C8 | #204 | semidirect |
| 150. C3 | #1590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#204 | 2 |
| #4688 | 2 |
| #4679 | 2 |
| C3×C82 | 2 |
| #4459 | 2 |
| #4457 | 2 |
| #4456 | 2 |
| #1590 | 3 |