Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5470 | C2 | semidirect |
| 3. #5228 | C2 | semidirect |
| 5. #5060 | C2 | semidirect |
| 6. #5055 | C2 | semidirect |
| 7. #5054 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 19. C2×#216 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 26. #869 | C22 | semidirect |
| 28. C4×Dic6 | C22 | semidirect |
| 29. #835 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. #803 | C22 | semidirect |
| 219. C3 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| #5470 | 2 |
| #5228 | 2 |
| #5218 | 2 |
| #5060 | 2 |
| #5055 | 2 |
| #5054 | 2 |
| #4926 | 2 |
| #3215 | 3 |