Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 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. C22×D3×Q8 | C2 | semidirect |
| 2. C2×C3×C4×Q8 | C2 | semidirect |
| 3. Q8×D12 | C2 | direct (N × H) |
| 4. C2×#897 | C2 | semidirect |
| 6. C2×#869 | C2 | semidirect |
| 10. C2×D3×Q8 | C22 | semidirect |
| 14. C3×C4×Q8 | C22 | semidirect |
| 20. #897 | C22 | semidirect |
| 22. #869 | C22 | semidirect |
| 27. C2×C4×Q8 | D3 | semidirect |
| 30. C2×C3×Q8 | D4 | semidirect |
| 37. C2×D12 | Q8 | direct (N × H) |
| 56. C4×Q8 | C2×D3 | semidirect |
| 66. C22×D3 | C2×Q8 | semidirect |
| 68. C3×Q8 | C2×D4 | semidirect |
| 71. C2×C3×C4 | C2×Q8 | semidirect |
| 77. D12 | C2×Q8 | direct (N × H) |
| 84. C2×Q8 | D12 | direct (N × H) |
| 106. C2×D3 | C22×Q8 | semidirect |
| 109. C3×C4 | C22×Q8 | semidirect |
| 117. Q8 | C2×D12 | direct (N × H) |
| 124. C2×C4 | D3×Q8 | semidirect |
| 128. C2×C3 | D4×Q8 | semidirect |
| 144. C4 | C2×D3×Q8 | semidirect |
| 145. C3 | C2×D4×Q8 | semidirect |
| 147. C2 | Q8×D12 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×C3×C4×Q8 | 2 |
| Q8×D12 | 2 |
| C2×#897 | 2 |
| C2×C4×D12 | 2 |
| C2×#869 | 2 |
| C2×D4×Q8 | 3 |