Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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×#441 | C2 | semidirect |
| 4. #4565 | C2 | semidirect |
| 6. #4487 | C2 | semidirect |
| 7. #4466 | C2 | semidirect |
| 16. #829 | C4 | semidirect |
| 17. #828 | C4 | semidirect |
| 24. #441 | D3 | semidirect |
| 125. C3 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#441 | 2 |
| #5179 | 2 |
| #4717 | 2 |
| #4565 | 2 |
| #4488 | 2 |
| #4487 | 2 |
| #4466 | 2 |
| #2180 | 3 |