Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. C22×C3×D8 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. C2×#833 | C2 | semidirect |
| 4. #5110 | C2 | semidirect |
| 5. #4552 | C2 | semidirect |
| 21. C22×D8 | D3 | semidirect |
| 163. C3 | #2018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×#932 | 2 |
| C2×#833 | 2 |
| #5110 | 2 |
| #4552 | 2 |
| #2018 | 3 |