Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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. #4998 | C2 | semidirect |
| 5. #4995 | C2 | semidirect |
| 6. #4964 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 14. #948 | C4 | semidirect |
| 50. #208 | C2×C4 | semidirect |
| 51. C2×C3⋊C8 | C2×C4 | semidirect |
| 148. C3 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#520 | 2 |
| #5827 | 2 |
| C2×#948 | 2 |
| #4998 | 2 |
| #4995 | 2 |
| #4964 | 2 |
| C2×#808 | 2 |
| #2912 | 3 |