Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #4699 | C2 | semidirect |
| 4. #4482 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 51. C3×D4 | Q16 | semidirect |
| 95. D4 | Dic12 | semidirect |
| 122. C3 | #1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| #5007 | 2 |
| #4699 | 2 |
| #4482 | 2 |
| #4458 | 2 |
| #1669 | 3 |