Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #5827 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. #5221 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 12. C3×AGL(1,ℤ/8) | C4 | semidirect |
| 48. C2×C3×D4 | C2×C4 | semidirect |
| 58. C3×M16 | C2×C4 | semidirect |
| 78. AGL(1,ℤ/8) | Dic3 | semidirect |
| 103. C3×Q8 | C22⋊C4 | semidirect |
| 111. C3×D4 | C22⋊C4 | semidirect |
| 143. C2×D4 | C2×Dic3 | semidirect |
| 155. M16 | C2×Dic3 | semidirect |
| 200. Q8 | #217 | semidirect |
| 208. D4 | #217 | semidirect |
| 257. C3 | #1883 | 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 |
| #5827 | 2 |
| C2×#837 | 2 |
| #5221 | 2 |
| #5215 | 2 |
| #4555 | 2 |
| #4554 | 2 |
| #1883 | 3 |