Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #4680 | C2 | semidirect |
| 4. #4494 | C2 | semidirect |
| 5. #4463 | C2 | semidirect |
| 23. C3×Q16 | Q8 | semidirect |
| 25. C3×D8 | Q8 | semidirect |
| 59. Q16 | Dic6 | semidirect |
| 61. D8 | Dic6 | semidirect |
| 101. C3 | #2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#443 | 2 |
| #4680 | 2 |
| #4566 | 2 |
| #4494 | 2 |
| #4463 | 2 |
| #2230 | 3 |