Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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×#557 | C2 | semidirect |
| 3. #5092 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #5030 | C2 | semidirect |
| 11. #5024 | C2 | semidirect |
| 42. #557 | D3 | semidirect |
| 234. C3 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5584 | 2 |
| #5092 | 2 |
| #5090 | 2 |
| #5086 | 2 |
| #5083 | 2 |
| #5031 | 2 |
| #5030 | 2 |
| #5028 | 2 |
| C4×#215 | 2 |
| #5024 | 2 |
| #3398 | 3 |