Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#948 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5234 | C2 | semidirect |
| 6. #4552 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 13. C2×C3×Q16 | C4 | semidirect |
| 14. C2×C3×SD16 | C4 | semidirect |
| 15. C2×C3×SD16 | C4 | semidirect |
| 16. C2×C3×D8 | C4 | semidirect |
| 81. C2×Q16 | Dic3 | semidirect |
| 82. C2×SD16 | Dic3 | semidirect |
| 83. C2×SD16 | Dic3 | semidirect |
| 84. C2×D8 | Dic3 | semidirect |
| 253. C3 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| C2×#948 | 2 |
| C2×#837 | 2 |
| #5234 | 2 |
| #4552 | 2 |
| #4550 | 2 |
| #1876 | 3 |