Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#216 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5052 | C2 | semidirect |
| 7. #5051 | C2 | semidirect |
| 8. #5004 | C2 | semidirect |
| 9. #4998 | C2 | semidirect |
| 226. C3 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| #5825 | 2 |
| C2×#948 | 2 |
| C22×#216 | 2 |
| #5225 | 2 |
| #5052 | 2 |
| #5051 | 2 |
| #5004 | 2 |
| #4998 | 2 |
| #3059 | 3 |