Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5091 | C2 | semidirect |
| 4. #5079 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 7. #4482 | C2 | semidirect |
| 168. C3 | #1638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5542 | 2 |
| C3×#476 | 2 |
| #5091 | 2 |
| #5079 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4484 | 2 |
| #4482 | 2 |
| #1638 | 3 |