Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 4. #5212 | C2 | semidirect |
| 5. #4984 | C2 | semidirect |
| 6. #4980 | C2 | semidirect |
| 7. #4951 | C2 | semidirect |
| 8. #4951 | C2 | semidirect |
| 9. #4950 | C2 | semidirect |
| 14. C3×#123 | C4 | semidirect |
| 49. C22×C3×C4 | C2×C4 | semidirect |
| 59. C3×C4⋊C4 | C2×C4 | semidirect |
| 61. C3×C22⋊C4 | C2×C4 | semidirect |
| 75. #123 | Dic3 | semidirect |
| 142. C22×C4 | C2×Dic3 | semidirect |
| 150. C4⋊C4 | C2×Dic3 | semidirect |
| 156. C22⋊C4 | C2×Dic3 | semidirect |
| 245. C3 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#123 | 2 |
| #5221 | 2 |
| #5220 | 2 |
| #5212 | 2 |
| #4984 | 2 |
| #4980 | 2 |
| #4951 | 2 |
| #4950 | 2 |
| #2376 | 3 |