Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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. D3×#99 | C2 | semidirect |
| 3. C3×#353 | C2 | semidirect |
| 4. #4545 | C2 | semidirect |
| 5. #4474 | C2 | semidirect |
| 8. C2×D3×D4 | C4 | semidirect |
| 12. #940 | C4 | semidirect |
| 15. #874 | C4 | semidirect |
| 16. C42×D3 | C4 | semidirect |
| 17. C3×#99 | C22 | semidirect |
| 18. #834 | C22 | semidirect |
| 24. #353 | D3 | direct (N × H) |
| 28. C2×C3×D4 | C2×C4 | semidirect |
| 41. C2×D12 | C2×C4 | semidirect |
| 46. C3×C42 | C2×C4 | semidirect |
| 50. C4×Dic3 | C2×C4 | semidirect |
| 63. #99 | C2×D3 | semidirect |
| 110. C2×D4 | C4×D3 | semidirect |
| 120. C42 | C4×D3 | semidirect |
| 181. D3 | #353 | direct (N × H) |
| 204. C3 | C2×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#127 | 2 |
| D3×#99 | 2 |
| C3×#353 | 2 |
| #4545 | 2 |
| #4474 | 2 |
| C2×#353 | 3 |