Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5543 | C2 | semidirect |
| 3. #5239 | C2 | semidirect |
| 4. #5232 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. #5042 | C2 | semidirect |
| 8. #5033 | C2 | semidirect |
| 9. C4×#216 | C2 | semidirect |
| 10. #5021 | C2 | semidirect |
| 11. #5012 | C2 | semidirect |
| 251. C3 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#550 | 2 |
| #5543 | 2 |
| #5239 | 2 |
| #5232 | 2 |
| #5075 | 2 |
| #5070 | 2 |
| #5042 | 2 |
| #5033 | 2 |
| C4×#216 | 2 |
| #5021 | 2 |
| #5012 | 2 |
| #3333 | 3 |