Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#137 | C2 | semidirect |
| 3. C2×#947 | C2 | semidirect |
| 4. C2×#942 | C2 | semidirect |
| 5. C2×#837 | C2 | semidirect |
| 6. #5202 | C2 | direct (N × H) |
| 7. C2×#825 | C2 | semidirect |
| 8. C2×#823 | C2 | semidirect |
| 11. C22×C3×Q8 | C22 | semidirect |
| 24. C3×#137 | C22 | semidirect |
| 27. C2×C3×M16 | C22 | semidirect |
| 29. #947 | C22 | semidirect |
| 32. #942 | C22 | semidirect |
| 35. C2×C4×Dic3 | C22 | semidirect |
| 36. C2×#208 | C22 | semidirect |
| 37. #837 | C22 | semidirect |
| 38. #825 | C22 | semidirect |
| 39. #823 | C22 | semidirect |
| 42. C2×#137 | D3 | semidirect |
| 60. C2×C3×Q8 | C23 | semidirect |
| 97. C3×M16 | C23 | semidirect |
| 103. C4×Dic3 | C23 | semidirect |
| 105. #208 | C23 | semidirect |
| 115. C22×Q8 | C2×D3 | semidirect |
| 123. #137 | C2×D3 | semidirect |
| 129. C2×M16 | C2×D3 | semidirect |
| 209. C2×Q8 | C22×D3 | semidirect |
| 241. M16 | C22×D3 | semidirect |
| 322. C2×C3 | #455 | semidirect |
| 347. C3 | C2×#455 | semidirect |
| 353. C2 | #5202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C2×C3×#137 | 2 |
| C2×#947 | 2 |
| C2×#942 | 2 |
| C2×#837 | 2 |
| #5202 | 2 |
| C2×#825 | 2 |
| C2×#823 | 2 |
| C2×#455 | 3 |