Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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. #4851 | C2 | semidirect |
| 5. #4849 | C2 | semidirect |
| 127. C3 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×#423 | 2 |
| #5137 | 2 |
| #4851 | 2 |
| #4849 | 2 |
| #3255 | 3 |