Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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×#870 | C2 | semidirect |
| 3. #5081 | C2 | semidirect |
| 4. #5071 | C2 | semidirect |
| 5. #5034 | C2 | semidirect |
| 6. #5033 | C2 | semidirect |
| 7. #5009 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 207. C3 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C2×#870 | 2 |
| #5081 | 2 |
| #5071 | 2 |
| #5034 | 2 |
| #5033 | 2 |
| #5009 | 2 |
| #4926 | 2 |
| #3234 | 3 |