Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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×#568 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #4557 | C2 | semidirect |
| 12. #947 | C4 | semidirect |
| 13. #940 | C4 | semidirect |
| 20. #568 | D3 | semidirect |
| 42. C2×C3×C8 | D4 | semidirect |
| 102. C2×C8 | #67 | semidirect |
| 165. C3 | #1910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| #5830 | 2 |
| #5240 | 2 |
| #5131 | 2 |
| #4557 | 2 |
| #1910 | 3 |