Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic6 | C2 | semidirect |
| 3. C2×#951 | C2 | semidirect |
| 4. #5207 | C2 | semidirect |
| 5. #5050 | C2 | semidirect |
| 6. #5040 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 24. C2×#216 | C22 | semidirect |
| 25. C2×#214 | C22 | semidirect |
| 28. #810 | C22 | semidirect |
| 57. C2×Dic6 | D4 | semidirect |
| 156. C22×C3 | #137 | semidirect |
| 203. C22 | #951 | semidirect |
| 211. C3 | #3004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C3×#525 | 2 |
| C2×#951 | 2 |
| #5207 | 2 |
| #5050 | 2 |
| #5040 | 2 |
| #5004 | 2 |
| #3004 | 3 |