Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5122 | C2 | semidirect |
| 5. #4559 | C2 | semidirect |
| 12. C2×#208 | C4 | semidirect |
| 14. C22×C3⋊C8 | C4 | semidirect |
| 16. C3×#101 | C4 | semidirect |
| 17. C3×#100 | C4 | semidirect |
| 57. #101 | Dic3 | semidirect |
| 58. #100 | Dic3 | semidirect |
| 144. C3 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#948 | 2 |
| C3×#413 | 2 |
| #5240 | 2 |
| #5122 | 2 |
| #4559 | 2 |
| #1757 | 3 |