Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #5081 | C2 | semidirect |
| 4. #5080 | C2 | semidirect |
| 5. #5078 | C2 | semidirect |
| 62. #208 | Q8 | semidirect |
| 103. C3⋊C8 | C2×Q8 | semidirect |
| 180. C3 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| #5470 | 2 |
| #5081 | 2 |
| #5080 | 2 |
| #5078 | 2 |
| #4964 | 2 |
| C4×#208 | 2 |
| #3165 | 3 |