Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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×#336 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 20. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 23. C2×D3×C8 | C4 | semidirect |
| 32. #336 | D3 | semidirect |
| 210. C3 | #1729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| C22×D3×C8 | 2 |
| C2×#872 | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| #1729 | 3 |