Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 80. C3⋊C8 | Q16 | semidirect |
| 139. C3 | #1584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#216 | 2 |
| Q8×C3⋊C8 | 2 |
| #4831 | 2 |
| C3×Q8⋊C8 | 2 |
| #4479 | 2 |
| #4456 | 2 |
| #4454 | 2 |
| #1584 | 3 |