Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 1. C22×#215 | C2 | semidirect |
| 3. C3×#391 | C2 | semidirect |
| 4. C2×#809 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 22. #391 | D3 | semidirect |
| 28. C2×C3×Q8 | D4 | semidirect |
| 47. C2×C3⋊C8 | D4 | semidirect |
| 75. C2×C3×C4 | SD16 | semidirect |
| 90. C2×Q8 | D12 | semidirect |
| 145. C2×C4 | #215 | semidirect |
| 172. C3 | #2014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#215 | 2 |
| C2×#874 | 2 |
| C3×#391 | 2 |
| C2×#809 | 2 |
| #4524 | 2 |
| #2014 | 3 |