Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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. C2×#807 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 13. C22×C3⋊C8 | C4 | semidirect |
| 78. C3⋊C8 | C22⋊C4 | semidirect |
| 103. C22×C3 | #107 | semidirect |
| 148. C22 | #807 | semidirect |
| 160. C3 | #1808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊C8 | 2 |
| C3×#380 | 2 |
| #5212 | 2 |
| C2×#807 | 2 |
| #4529 | 2 |
| #1808 | 3 |