Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 3. C3×#354 | C2 | semidirect |
| 4. #4541 | C2 | semidirect |
| 5. #4473 | C2 | semidirect |
| 7. C2×D3×Q8 | C4 | semidirect |
| 10. #947 | C4 | semidirect |
| 15. #875 | C4 | semidirect |
| 16. C42×D3 | C4 | semidirect |
| 24. #354 | D3 | direct (N × H) |
| 26. C2×C3×Q8 | C2×C4 | semidirect |
| 39. C2×Dic6 | C2×C4 | semidirect |
| 42. C3×C42 | C2×C4 | semidirect |
| 49. C4×Dic3 | C2×C4 | semidirect |
| 94. C2×Q8 | C4×D3 | semidirect |
| 113. C42 | C4×D3 | semidirect |
| 163. D3 | #354 | direct (N × H) |
| 182. C3 | C2×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#124 | 2 |
| D3×#99 | 2 |
| C3×#354 | 2 |
| #4541 | 2 |
| #4473 | 2 |
| C2×#354 | 3 |