Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#833 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 11. C2×#208 | C22 | semidirect |
| 89. C22×C3 | #100 | semidirect |
| 128. C22 | #833 | semidirect |
| 133. C3 | #1783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C2×#833 | 2 |
| #5207 | 2 |
| #1783 | 3 |