Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 213 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. #5000 | C2 | semidirect |
| 4. #4924 | C2 | semidirect |
| 5. C4×#208 | C2 | semidirect |
| 16. C4⋊(C3⋊C8) | C22 | semidirect |
| 17. #803 | C22 | semidirect |
| 18. C4×C3⋊C8 | C22 | semidirect |
| 126. C3 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| #5207 | 2 |
| #5000 | 2 |
| #4924 | 2 |
| C4×#208 | 2 |
| #2921 | 3 |