Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
278 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 97 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×#822 | C2 | semidirect |
| 5. #4558 | C2 | semidirect |
| 111. C22×C3 | #108 | semidirect |
| 156. C22 | #822 | semidirect |
| 164. C3 | #1855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| #5207 | 2 |
| C2×#830 | 2 |
| C2×#822 | 2 |
| #4558 | 2 |
| #1855 | 3 |