Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. C22×#214 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×#887 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4762 | C2 | direct (N × H) |
| 20. C2×#214 | C22 | semidirect |
| 26. C2×#204 | C22 | semidirect |
| 28. #887 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. Dic3⋊C8 | C22 | semidirect |
| 31. #809 | C22 | semidirect |
| 39. C2×#102 | D3 | semidirect |
| 61. C2×Dic6 | D4 | semidirect |
| 96. #102 | C2×D3 | semidirect |
| 120. C2×Dic3 | SD16 | semidirect |
| 128. Dic6 | C2×D4 | semidirect |
| 184. Dic3 | C2×SD16 | semidirect |
| 220. C2×C3 | #460 | semidirect |
| 244. C3 | C2×#460 | semidirect |
| 247. C2 | #4762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| C22×#214 | 2 |
| C22×#204 | 2 |
| C2×#887 | 2 |
| C2×C3×#102 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#809 | 2 |
| #4762 | 2 |
| C2×#460 | 3 |