Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×C3×#104 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5129 | C2 | semidirect |
| 5. C2×#822 | C2 | semidirect |
| 6. C2×#805 | C2 | semidirect |
| 7. C2×#803 | C2 | semidirect |
| 15. C2×#216 | C4 | semidirect |
| 16. C2×#215 | C4 | semidirect |
| 17. C2×#214 | C4 | semidirect |
| 18. C2×#213 | C4 | semidirect |
| 31. C2×#104 | D3 | semidirect |
| 232. C3 | #1975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#950 | 2 |
| C2×C3×#104 | 2 |
| #5234 | 2 |
| #5129 | 2 |
| C2×#822 | 2 |
| C2×#805 | 2 |
| C2×#803 | 2 |
| #1975 | 3 |