Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×#208 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. #5212 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 11. C3×#121 | C4 | semidirect |
| 51. C2×C3⋊C8 | D4 | semidirect |
| 59. #121 | Dic3 | semidirect |
| 201. C3 | #1895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| C22×#208 | 2 |
| C2×#832 | 2 |
| #5212 | 2 |
| #4529 | 2 |
| #1895 | 3 |