Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C3×#494 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 5. #5079 | C2 | semidirect |
| 7. #4680 | C2 | semidirect |
| 27. #494 | D3 | semidirect |
| 133. C3 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C3×#494 | 2 |
| #5189 | 2 |
| #5184 | 2 |
| #5079 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| #4680 | 2 |
| #3185 | 3 |