Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×C3×Q8 | C2 | semidirect |
| 3. C22×#216 | C2 | semidirect |
| 4. C2×#942 | C2 | direct (N × H) |
| 5. C22×#215 | C2 | semidirect |
| 6. C22×#208 | C2 | semidirect |
| 11. C22×C3×Q8 | C22 | semidirect |
| 20. C2×#216 | C22 | semidirect |
| 21. #942 | C22 | direct (N × H) |
| 22. C2×#215 | C22 | semidirect |
| 23. C2×#208 | C22 | semidirect |
| 26. C23×Q8 | D3 | semidirect |
| 37. C2×C3×Q8 | C23 | semidirect |
| 53. #216 | C23 | semidirect |
| 54. #215 | C23 | semidirect |
| 55. #208 | C23 | semidirect |
| 63. C22×Q8 | C2×D3 | semidirect |
| 107. C2×Q8 | C22×D3 | semidirect |
| 124. C22×C3 | #137 | semidirect |
| 158. C2×C3 | C2×#137 | semidirect |
| 164. C22 | #942 | direct (N × H) |
| 172. C3 | C22×#137 | semidirect |
| 175. C2 | C2×#942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C22×#235 | 2 |
| C22×#216 | 2 |
| C2×#942 | 2 |
| C22×#215 | 2 |
| C22×#208 | 2 |
| C22×#137 | 3 |