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 |
|---|---|---|
| 1. C2×C3×#137 | C2 | semidirect |
| 3. C2×#942 | C2 | semidirect |
| 4. #5745 | C2 | semidirect |
| 5. #5237 | C2 | semidirect |
| 6. C2×#836 | C2 | semidirect |
| 7. #5192 | C2 | semidirect |
| 8. #5177 | C2 | semidirect |
| 9. #5125 | C2 | semidirect |
| 16. C2×C3×Q16 | C22 | semidirect |
| 17. C2×C3×SD16 | C22 | semidirect |
| 34. #836 | C22 | semidirect |
| 35. #836 | C22 | semidirect |
| 36. #833 | C22 | semidirect |
| 37. #819 | C22 | semidirect |
| 40. C2×#137 | D3 | semidirect |
| 106. C2×Q16 | C2×D3 | semidirect |
| 108. C2×SD16 | C2×D3 | semidirect |
| 278. C3 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5822 | 2 |
| C2×#942 | 2 |
| #5745 | 2 |
| #5237 | 2 |
| C2×#836 | 2 |
| #5192 | 2 |
| #5177 | 2 |
| #5125 | 2 |
| #3069 | 3 |