Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #5570 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4856 | C2 | semidirect |
| 8. #4793 | C2 | semidirect |
| 10. #4682 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 62. C3×SD16 | Q8 | semidirect |
| 116. C3×Q8 | C2×Q8 | semidirect |
| 136. C3×C8 | C2×Q8 | semidirect |
| 147. SD16 | Dic6 | semidirect |
| 191. Q8 | C2×Dic6 | semidirect |
| 208. C8 | C2×Dic6 | semidirect |
| 228. C3 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5570 | 2 |
| D4×Dic6 | 2 |
| C3×C4×SD16 | 2 |
| #5164 | 2 |
| #5020 | 2 |
| #5007 | 2 |
| #4856 | 2 |
| #4793 | 2 |
| #4766 | 2 |
| #4682 | 2 |
| #4679 | 2 |
| #3386 | 3 |