Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
| 4. #5009 | C2 | semidirect |
| 5. #5008 | C2 | semidirect |
| 6. #5007 | C2 | semidirect |
| 7. #4964 | C2 | semidirect |
| 8. #4924 | C2 | semidirect |
| 23. #870 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 30. #808 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 45. C2×C3×D4 | Q8 | semidirect |
| 130. C2×D4 | Dic6 | semidirect |
| 225. C3 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| #5470 | 2 |
| #5215 | 2 |
| #5009 | 2 |
| #5008 | 2 |
| #5007 | 2 |
| #4964 | 2 |
| #4924 | 2 |
| #3077 | 3 |