Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 6. #4702 | C2 | semidirect |
| 7. #4683 | C2 | semidirect |
| 8. #4680 | C2 | semidirect |
| 40. C3×M16 | Q8 | semidirect |
| 41. C2×C3×C8 | Q8 | semidirect |
| 93. M16 | Dic6 | semidirect |
| 94. C2×C8 | Dic6 | semidirect |
| 147. C3 | #3163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5519 | 2 |
| C3×#405 | 2 |
| #5121 | 2 |
| #5106 | 2 |
| C2×#817 | 2 |
| #4702 | 2 |
| #4683 | 2 |
| #4680 | 2 |
| #3163 | 3 |