Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C4⋊(C3⋊C16) | C2 | semidirect |
| 4. #4461 | C2 | semidirect |
| 110. C3 | #2163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C8 | 2 |
| #4549 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #4461 | 2 |
| #2163 | 3 |