Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×Dic6 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 7. #4854 | C2 | semidirect |
| 8. #4789 | C2 | semidirect |
| 10. #4681 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 228. C3 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic6 | 2 |
| #5542 | 2 |
| C3×C4×SD16 | 2 |
| #5166 | 2 |
| #5031 | 2 |
| #5008 | 2 |
| #4854 | 2 |
| #4789 | 2 |
| #4765 | 2 |
| #4681 | 2 |
| #4679 | 2 |
| #3369 | 3 |