Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 39. C3×M16 | Q8 | semidirect |
| 57. C4×Dic3 | Q8 | semidirect |
| 59. #208 | Q8 | semidirect |
| 107. M16 | Dic6 | semidirect |
| 185. C3 | #2061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5519 | 2 |
| C3×#428 | 2 |
| #4977 | 2 |
| #4964 | 2 |
| #4555 | 2 |
| #4554 | 2 |
| #4532 | 2 |
| #2061 | 3 |