Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #5182 | C2 | semidirect |
| 7. #4854 | C2 | semidirect |
| 8. #4795 | C2 | semidirect |
| 9. #4791 | C2 | semidirect |
| 195. C3 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5622 | 2 |
| C3×#470 | 2 |
| #5182 | 2 |
| #5137 | 2 |
| #5118 | 2 |
| #5052 | 2 |
| #4854 | 2 |
| #4795 | 2 |
| #4791 | 2 |
| #3255 | 3 |