Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 136. Dic6 | Q16 | semidirect |
| 227. C3 | #3395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5721 | 2 |
| #5567 | 2 |
| C3×#462 | 2 |
| #5183 | 2 |
| #5182 | 2 |
| #5092 | 2 |
| C4×#216 | 2 |
| #4849 | 2 |
| #4830 | 2 |
| #4795 | 2 |
| #4790 | 2 |
| #3395 | 3 |