Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 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×SD16 | C2 | semidirect |
| 2. C2×#946 | C2 | semidirect |
| 4. C2×#835 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 30. C22×SD16 | D3 | semidirect |
| 44. C2×C3×Q8 | D4 | semidirect |
| 68. C2×C3×C8 | D4 | semidirect |
| 74. C4⋊Dic3 | D4 | semidirect |
| 114. C22×D3 | SD16 | semidirect |
| 155. C2×Q8 | #67 | semidirect |
| 182. C2×C8 | #67 | semidirect |
| 305. C3 | #2000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SD16 | 2 |
| C2×#946 | 2 |
| C2×#938 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4551 | 2 |
| #2000 | 3 |