Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #5567 | C2 | semidirect |
| 3. C3×C8×Q8 | C2 | semidirect |
| 4. #4850 | C2 | semidirect |
| 7. #4829 | C2 | semidirect |
| 10. #4683 | C2 | semidirect |
| 11. #4680 | C2 | semidirect |
| 50. C8×Q8 | D3 | semidirect |
| 83. #204 | Q8 | semidirect |
| 224. C3 | #3381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| #5567 | 2 |
| C3×C8×Q8 | 2 |
| #4850 | 2 |
| #4847 | 2 |
| #4846 | 2 |
| #4829 | 2 |
| C4×#204 | 2 |
| #4683 | 2 |
| #4680 | 2 |
| #3381 | 3 |