Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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. #4699 | C2 | semidirect |
| 4. #4496 | C2 | semidirect |
| 5. #4463 | C2 | semidirect |
| 113. C3 | #2214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#443 | 2 |
| #5195 | 2 |
| #4699 | 2 |
| #4496 | 2 |
| #4463 | 2 |
| #2214 | 3 |