Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. C2×#817 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 224. C3 | #2077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊C8 | 2 |
| #5212 | 2 |
| C2×#817 | 2 |
| #4551 | 2 |
| #2077 | 3 |