Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. Q8×C3⋊C8 | C2 | semidirect |
| 4. #4535 | C2 | semidirect |
| 6. #4458 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 66. C3×Q8 | M16 | semidirect |
| 116. Q8 | #208 | semidirect |
| 150. C3 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×SD16 | 2 |
| Q8×C3⋊C8 | 2 |
| #5012 | 2 |
| #4535 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4458 | 2 |
| #4454 | 2 |
| #1588 | 3 |