Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. C3×C4×Q16 | C2 | semidirect |
| 3. #5189 | C2 | semidirect |
| 4. #5022 | C2 | semidirect |
| 5. #4881 | C2 | semidirect |
| 6. #4814 | C2 | semidirect |
| 7. #4811 | C2 | semidirect |
| 9. #4683 | C2 | semidirect |
| 42. C4×Q16 | D3 | semidirect |
| 188. C3 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5581 | 2 |
| C3×C4×Q16 | 2 |
| #5189 | 2 |
| #5022 | 2 |
| #4881 | 2 |
| #4814 | 2 |
| #4811 | 2 |
| #4688 | 2 |
| #4683 | 2 |
| #3352 | 3 |