Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#822 | C2 | semidirect |
| 4. C3×#341 | C2 | semidirect |
| 5. #4552 | C2 | semidirect |
| 20. #341 | D3 | semidirect |
| 124. C3 | #1811 | 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 |
| #5126 | 2 |
| C2×#822 | 2 |
| C3×#341 | 2 |
| #4552 | 2 |
| #1811 | 3 |