Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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. #5798 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5236 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #4557 | C2 | semidirect |
| 7. #4556 | C2 | semidirect |
| 13. C2×C3×SD16 | C4 | semidirect |
| 14. C2×C3×D8 | C4 | semidirect |
| 38. C2×C3×Q8 | C2×C4 | semidirect |
| 44. C2×C3×D4 | C2×C4 | semidirect |
| 54. C2×C3×C8 | C2×C4 | semidirect |
| 72. C2×SD16 | Dic3 | semidirect |
| 73. C2×D8 | Dic3 | semidirect |
| 121. C2×Q8 | C2×Dic3 | semidirect |
| 127. C2×D4 | C2×Dic3 | semidirect |
| 140. C2×C8 | C2×Dic3 | semidirect |
| 224. C3 | #1904 | 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 |
| #5798 | 2 |
| #5240 | 2 |
| #5236 | 2 |
| #5215 | 2 |
| #4557 | 2 |
| #4556 | 2 |
| #1904 | 3 |