Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 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. C2×C3×C4×Q8 | C2 | semidirect |
| 3. #5227 | C2 | semidirect |
| 4. #5027 | C2 | semidirect |
| 5. #5026 | C2 | semidirect |
| 6. #5021 | C2 | semidirect |
| 7. #4967 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 35. C2×C4×Q8 | D3 | semidirect |
| 101. C3×Q8 | #41 | semidirect |
| 175. Q8 | #235 | semidirect |
| 217. C3 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| #5477 | 2 |
| #5227 | 2 |
| #5027 | 2 |
| #5026 | 2 |
| #5021 | 2 |
| #4967 | 2 |
| #4926 | 2 |
| #3112 | 3 |