Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 117 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. #4458 | C2 | semidirect |
| 4. #4457 | C2 | semidirect |
| 24. C2×C3×C8 | C8 | semidirect |
| 65. C2×C8 | C3⋊C8 | semidirect |
| 116. C3 | #1564 | 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 |
| #4925 | 2 |
| #4458 | 2 |
| #4457 | 2 |
| #1564 | 3 |