Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×C3×C4×C8 | C2 | semidirect |
| 5. #4928 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 22. #821 | C4 | semidirect |
| 25. C2×C4×C8 | D3 | semidirect |
| 228. C3 | #1934 | 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 |
| C2×#821 | 2 |
| #4939 | 2 |
| #4928 | 2 |
| #4551 | 2 |
| #1934 | 3 |