Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 382 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. #5516 | C2 | semidirect |
| 3. #5075 | C2 | semidirect |
| 4. #5063 | C2 | semidirect |
| 5. #5040 | C2 | semidirect |
| 6. #5035 | C2 | semidirect |
| 7. #5018 | C2 | semidirect |
| 8. C4×#214 | C2 | semidirect |
| 9. #5000 | C2 | semidirect |
| 198. C3 | #3126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#540 | 2 |
| #5516 | 2 |
| #5075 | 2 |
| #5063 | 2 |
| #5040 | 2 |
| #5035 | 2 |
| #5018 | 2 |
| C4×#214 | 2 |
| #5000 | 2 |
| #3126 | 3 |