Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C3×#334 | C2 | semidirect |
| 5. #4480 | C2 | semidirect |
| 6. #4479 | C2 | semidirect |
| 7. #4458 | C2 | semidirect |
| 30. #334 | D3 | semidirect |
| 47. ΓL(1,𝔽25) | C8 | semidirect |
| 79. C3×C8 | C2×C8 | semidirect |
| 83. C3⋊C8 | C2×C8 | semidirect |
| 133. C8 | D3×C8 | semidirect |
| 150. C3 | #1565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4833 | 2 |
| D3×C4⋊C8 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| C3×#334 | 2 |
| #4480 | 2 |
| #4479 | 2 |
| #4458 | 2 |
| #1565 | 3 |