Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C3×C22⋊Q8 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 4. C2×#835 | C2 | semidirect |
| 5. C2×#830 | C2 | semidirect |
| 6. C2×#809 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 31. C2×C22⋊Q8 | D3 | semidirect |
| 44. C2×C3×Q8 | D4 | semidirect |
| 67. C3×C4⋊C4 | D4 | semidirect |
| 78. C2×C3⋊C8 | D4 | semidirect |
| 106. C23×C3 | SD16 | semidirect |
| 155. C2×Q8 | #67 | semidirect |
| 187. C4⋊C4 | #67 | semidirect |
| 232. C23 | #215 | semidirect |
| 305. C3 | #2000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊Q8 | 2 |
| C22×#215 | 2 |
| C2×#930 | 2 |
| C2×#835 | 2 |
| C2×#830 | 2 |
| C2×#809 | 2 |
| #4529 | 2 |
| #2000 | 3 |