Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 4. #4964 | C2 | direct (N × H) |
| 5. C2×#808 | C2 | semidirect |
| 6. C2×#807 | C2 | semidirect |
| 20. C2×#208 | C4 | semidirect |
| 23. #808 | C22 | semidirect |
| 24. #807 | C22 | semidirect |
| 52. #208 | C2×C4 | semidirect |
| 53. C2×C3⋊C8 | C2×C4 | semidirect |
| 93. C3⋊C8 | C22×C4 | semidirect |
| 156. C2×C3 | #428 | semidirect |
| 175. C3 | C2×#428 | semidirect |
| 177. C2 | #4964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C2×#926 | 2 |
| C22×#208 | 2 |
| #4964 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| C2×#428 | 3 |