Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×C3×C4⋊Q8 | C2 | semidirect |
| 3. #5088 | C2 | direct (N × H) |
| 4. C2×#809 | C2 | semidirect |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 19. #809 | C22 | semidirect |
| 20. C4×C3⋊C8 | C22 | semidirect |
| 21. C2×C4⋊Q8 | D3 | semidirect |
| 53. C4⋊Q8 | C2×D3 | semidirect |
| 135. C2×C3 | #486 | semidirect |
| 153. C3 | C2×#486 | semidirect |
| 155. C2 | #5088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C2×#874 | 2 |
| #5088 | 2 |
| C2×#809 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#486 | 3 |