Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C3×C4×#41 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#874 | C2 | semidirect |
| 4. #5027 | C2 | semidirect |
| 5. #5015 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4924 | C2 | semidirect |
| 12. C3×C4×Q8 | C22 | semidirect |
| 14. C3×C4×D4 | C22 | semidirect |
| 20. C2×#215 | C22 | semidirect |
| 21. C2×#213 | C22 | semidirect |
| 26. #809 | C22 | semidirect |
| 27. C4⋊(C3⋊C8) | C22 | semidirect |
| 30. C4×#41 | D3 | semidirect |
| 37. C3×#41 | D4 | semidirect |
| 75. C4×Q8 | C2×D3 | semidirect |
| 77. C4×D4 | C2×D3 | semidirect |
| 90. C3×Q8 | C2×D4 | semidirect |
| 93. C3×D4 | C2×D4 | semidirect |
| 113. #41 | D12 | semidirect |
| 153. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 162. Q8 | C2×D12 | semidirect |
| 170. D4 | C2×D12 | semidirect |
| 200. C4 | #949 | semidirect |
| 203. C3 | #3038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| C2×#949 | 2 |
| C2×#874 | 2 |
| #5027 | 2 |
| #5015 | 2 |
| #5001 | 2 |
| #4924 | 2 |
| #3038 | 3 |