Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 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. C22×C3×D8 | C2 | semidirect |
| 2. C2×#940 | C2 | semidirect |
| 3. C22×#213 | C2 | semidirect |
| 4. #5221 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 29. C22×D8 | D3 | semidirect |
| 49. C2×C3×D4 | D4 | semidirect |
| 65. C2×C3×C8 | D4 | semidirect |
| 74. C2×C3⋊C8 | D4 | semidirect |
| 129. C2×Dic3 | D8 | semidirect |
| 159. C2×D4 | #67 | semidirect |
| 170. C2×C8 | #67 | semidirect |
| 278. C3 | #2011 | 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×#940 | 2 |
| C22×#213 | 2 |
| #5221 | 2 |
| C2×#832 | 2 |
| C2×#821 | 2 |
| #4550 | 2 |
| #2011 | 3 |