Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×C4×C4⋊C4 | C2 | semidirect |
| 4. C2×#807 | C2 | semidirect |
| 6. #4529 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 21. #809 | C4 | semidirect |
| 27. C4×C4⋊C4 | D3 | semidirect |
| 228. C3 | #1925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊C4 | 2 |
| C2×#809 | 2 |
| C2×#807 | 2 |
| #4939 | 2 |
| #4529 | 2 |
| #4524 | 2 |
| #1925 | 3 |