Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
| 2. C22×#216 | C2 | semidirect |
| 5. #5086 | C2 | direct (N × H) |
| 6. C2×#803 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 16. C2×#216 | C22 | semidirect |
| 23. #803 | C22 | semidirect |
| 26. C2×C4⋊Q8 | D3 | semidirect |
| 62. C4⋊Q8 | C2×D3 | semidirect |
| 145. C2×C3 | #497 | semidirect |
| 160. C3 | C2×#497 | semidirect |
| 162. C2 | #5086 | 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 |
| C22×#216 | 2 |
| C22×#215 | 2 |
| C2×#875 | 2 |
| #5086 | 2 |
| C2×#803 | 2 |
| C2×#497 | 3 |