Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#951 | C2 | semidirect |
| 3. C2×#951 | C2 | semidirect |
| 4. #5819 | C2 | semidirect |
| 5. #5237 | C2 | semidirect |
| 6. #5204 | C2 | semidirect |
| 7. #5200 | C2 | semidirect |
| 8. C2×#824 | C2 | semidirect |
| 9. #5124 | C2 | semidirect |
| 27. C2×#216 | C22 | semidirect |
| 29. C2×#214 | C22 | semidirect |
| 34. #836 | C22 | semidirect |
| 35. #833 | C22 | semidirect |
| 36. #824 | C22 | semidirect |
| 37. #822 | C22 | semidirect |
| 278. C3 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#575 | 2 |
| C2×#951 | 2 |
| #5819 | 2 |
| #5237 | 2 |
| #5204 | 2 |
| #5200 | 2 |
| C2×#824 | 2 |
| #5124 | 2 |
| #3069 | 3 |