Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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×Q16 | C2 | semidirect |
| 3. C2×#835 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 20. C22×Q16 | D3 | semidirect |
| 67. C22×D3 | Q16 | semidirect |
| 178. C3 | #2001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×#946 | 2 |
| C2×#835 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4551 | 2 |
| #2001 | 3 |