Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 20. #803 | C4 | semidirect |
| 21. C4×C3⋊C8 | C4 | semidirect |
| 152. C3 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#822 | 2 |
| #4998 | 2 |
| #4997 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4559 | 2 |
| #4533 | 2 |
| #4531 | 2 |
| #1833 | 3 |