Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×C3×Q16 | C2 | semidirect |
| 3. #5816 | C2 | semidirect |
| 4. C2×#942 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5187 | C2 | semidirect |
| 7. #5186 | C2 | semidirect |
| 8. #5113 | C2 | semidirect |
| 9. #5110 | C2 | semidirect |
| 40. C22×Q16 | D3 | semidirect |
| 275. C3 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| C22×C3×Q16 | 2 |
| #5816 | 2 |
| C2×#942 | 2 |
| #5225 | 2 |
| #5187 | 2 |
| #5186 | 2 |
| #5113 | 2 |
| #5110 | 2 |
| #3011 | 3 |