Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. C3×#362 | C2 | semidirect |
| 4. #4565 | C2 | semidirect |
| 6. #4513 | C2 | semidirect |
| 7. #4494 | C2 | semidirect |
| 25. #362 | D3 | semidirect |
| 119. C3 | #2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5189 | 2 |
| #4893 | 2 |
| C3×#362 | 2 |
| #4565 | 2 |
| #4514 | 2 |
| #4513 | 2 |
| #4494 | 2 |
| #2239 | 3 |