Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C2×#829 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4492 | C2 | semidirect |
| 7. #4489 | C2 | semidirect |
| 98. C22×C3 | Q32 | semidirect |
| 129. C22 | #829 | semidirect |
| 138. C3 | #2216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#467 | 2 |
| C2×#829 | 2 |
| #5116 | 2 |
| C22×C3⋊C16 | 2 |
| #4564 | 2 |
| #4492 | 2 |
| #4489 | 2 |
| #2216 | 3 |