Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 20. #817 | C4 | semidirect |
| 185. C3 | #1919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#817 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4972 | 2 |
| C3×#340 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #1919 | 3 |