Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 293 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. #4999 | C2 | semidirect |
| 4. #4924 | C2 | semidirect |
| 16. C4⋊(C3⋊C8) | C22 | semidirect |
| 122. C3 | #2905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| C22×#208 | 2 |
| #4999 | 2 |
| #4924 | 2 |
| #2905 | 3 |