Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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×C3×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #5822 | C2 | semidirect |
| 3. #5805 | C2 | semidirect |
| 4. #5240 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5139 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 33. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 44. C2×C3×Q8 | D4 | semidirect |
| 52. C2×C3×D4 | D4 | semidirect |
| 67. C3×M16 | D4 | semidirect |
| 82. C2×C3⋊C8 | D4 | semidirect |
| 156. C2×Q8 | #67 | semidirect |
| 167. C2×D4 | #67 | semidirect |
| 180. M16 | #67 | semidirect |
| 277. C3 | #2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5822 | 2 |
| #5805 | 2 |
| #5240 | 2 |
| #5215 | 2 |
| #5139 | 2 |
| #4559 | 2 |
| #2008 | 3 |