Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 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×#904 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. #4699 | C2 | semidirect |
| 5. #4696 | C2 | semidirect |
| 6. #4695 | C2 | semidirect |
| 7. #4693 | C2 | semidirect |
| 30. C2×C4×C8 | D3 | semidirect |
| 39. C2×C3×C8 | D4 | semidirect |
| 92. C2×C8 | D12 | semidirect |
| 107. C3×C4 | #135 | semidirect |
| 138. C4 | #904 | semidirect |
| 140. C3 | #3147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5477 | 2 |
| C2×C3×C4×C8 | 2 |
| #4699 | 2 |
| #4696 | 2 |
| #4695 | 2 |
| #4693 | 2 |
| #3147 | 3 |