Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 1. C22×Dic12 | C2 | semidirect |
| 4. C2×#869 | C2 | semidirect |
| 5. C2×C3×#97 | C2 | semidirect |
| 6. #4715 | C2 | direct (N × H) |
| 16. C2×Dic12 | C22 | semidirect |
| 22. #869 | C22 | semidirect |
| 23. C3×#97 | C22 | semidirect |
| 29. C2×#97 | D3 | semidirect |
| 68. #97 | C2×D3 | semidirect |
| 145. C2×C3 | #497 | semidirect |
| 160. C3 | C2×#497 | semidirect |
| 162. C2 | #4715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic12 | 2 |
| C22×#204 | 2 |
| C2×#875 | 2 |
| C2×#869 | 2 |
| C2×C3×#97 | 2 |
| #4715 | 2 |
| C2×#497 | 3 |