Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5570 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5164 | C2 | semidirect |
| 5. #5163 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. C4×#215 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 10. #4766 | C2 | semidirect |
| 11. #4764 | C2 | semidirect |
| 49. #460 | D3 | semidirect |
| 118. C3×Q8 | #41 | semidirect |
| 198. Q8 | #237 | semidirect |
| 243. C3 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5718 | 2 |
| #5570 | 2 |
| C3×#460 | 2 |
| #5164 | 2 |
| #5163 | 2 |
| #5070 | 2 |
| C4×#215 | 2 |
| #4846 | 2 |
| #4831 | 2 |
| #4766 | 2 |
| #4764 | 2 |
| #3368 | 3 |