Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #5825 | C2 | semidirect |
| 3. C2×#875 | C2 | semidirect |
| 4. C2×C3×#104 | C2 | semidirect |
| 5. C2×#824 | C2 | semidirect |
| 6. #5131 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 33. C2×#104 | D3 | semidirect |
| 254. C3 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5825 | 2 |
| C2×#949 | 2 |
| C2×#875 | 2 |
| C2×C3×#104 | 2 |
| C2×#824 | 2 |
| #5131 | 2 |
| #4523 | 2 |
| #2003 | 3 |