Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#908 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×#874 | C2 | semidirect |
| 4. C3×C4×M16 | C2 | semidirect |
| 5. #4712 | C2 | semidirect |
| 6. #4695 | C2 | semidirect |
| 7. #4693 | C2 | semidirect |
| 16. C2×D24 | C22 | semidirect |
| 17. C2×#204 | C22 | semidirect |
| 18. #875 | C22 | semidirect |
| 22. #874 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. C3×#97 | C22 | semidirect |
| 26. C3×C4×C8 | C22 | semidirect |
| 33. C4×M16 | D3 | semidirect |
| 49. C3×M16 | D4 | semidirect |
| 74. #97 | C2×D3 | semidirect |
| 75. C4×C8 | C2×D3 | semidirect |
| 97. C3×C8 | C2×D4 | semidirect |
| 115. M16 | D12 | semidirect |
| 132. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 156. C8 | C2×D12 | semidirect |
| 173. C4 | #908 | semidirect |
| 175. C3 | #3151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#908 | 2 |
| #5477 | 2 |
| C2×#874 | 2 |
| C3×C4×M16 | 2 |
| #4712 | 2 |
| #4695 | 2 |
| #4693 | 2 |
| #3151 | 3 |