Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 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. #5090 | C2 | semidirect |
| 4. #5063 | C2 | semidirect |
| 7. #5030 | C2 | semidirect |
| 8. C4×#216 | C2 | semidirect |
| 187. C3 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#541 | 2 |
| #5516 | 2 |
| #5090 | 2 |
| #5063 | 2 |
| #5050 | 2 |
| #5045 | 2 |
| #5030 | 2 |
| C4×#216 | 2 |
| #5000 | 2 |
| #3127 | 3 |