Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #5092 | C2 | semidirect |
| 4. #5082 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 6. #5065 | C2 | semidirect |
| 9. #5030 | C2 | semidirect |
| 10. C4×#216 | C2 | semidirect |
| 201. C3 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#541 | 2 |
| #5518 | 2 |
| #5092 | 2 |
| #5082 | 2 |
| #5069 | 2 |
| #5065 | 2 |
| #5052 | 2 |
| #5051 | 2 |
| #5030 | 2 |
| C4×#216 | 2 |
| #4997 | 2 |
| #3177 | 3 |