Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #5713 | C2 | semidirect |
| 3. #5075 | C2 | semidirect |
| 4. #4544 | C2 | semidirect |
| 5. #4456 | C2 | semidirect |
| 124. C3 | #1620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5713 | 2 |
| C3×#493 | 2 |
| #5075 | 2 |
| #4544 | 2 |
| #4456 | 2 |
| #1620 | 3 |