Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. #5830 | C2 | semidirect |
| 3. C2×#940 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. C2×#823 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 30. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 43. C2×C3×Q8 | D4 | semidirect |
| 50. C2×C3×D4 | D4 | semidirect |
| 51. C2×C3×D4 | D4 | semidirect |
| 67. C3×M16 | D4 | semidirect |
| 71. C4⋊Dic3 | D4 | semidirect |
| 74. C4×Dic3 | D4 | semidirect |
| 145. C2×Q8 | #67 | semidirect |
| 161. C2×D4 | #67 | semidirect |
| 162. C2×D4 | #67 | semidirect |
| 171. M16 | #67 | semidirect |
| 269. C3 | #2002 | 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 |
| #5830 | 2 |
| C2×#940 | 2 |
| C2×#837 | 2 |
| #5215 | 2 |
| C2×#823 | 2 |
| #4555 | 2 |
| #2002 | 3 |