Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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. C3×#341 | C2 | semidirect |
| 4. #4558 | C2 | semidirect |
| 5. #4552 | C2 | semidirect |
| 22. #341 | D3 | semidirect |
| 134. C3 | #1738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C3×#341 | 2 |
| #4558 | 2 |
| #4552 | 2 |
| #1738 | 3 |