Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×Dic6 | C2 | semidirect |
| 5. C22×C4⋊Dic3 | C2 | semidirect |
| 6. C22×Dic3⋊C4 | C2 | semidirect |
| 7. C22×Dic3⋊C4 | C2 | semidirect |
| 8. C2×#878 | C2 | direct (N × H) |
| 20. C22×Dic6 | C22 | semidirect |
| 23. C2×C4⋊Dic3 | C22 | semidirect |
| 24. C2×Dic3⋊C4 | C22 | semidirect |
| 25. C2×Dic3⋊C4 | C22 | semidirect |
| 26. #878 | C22 | direct (N × H) |
| 37. C24×C3 | Q8 | semidirect |
| 55. C2×Dic6 | C23 | semidirect |
| 58. C4⋊Dic3 | C23 | semidirect |
| 59. Dic3⋊C4 | C23 | semidirect |
| 60. Dic3⋊C4 | C23 | semidirect |
| 83. C23×C3 | C2×Q8 | semidirect |
| 103. C24 | Dic6 | semidirect |
| 130. C22×C3 | C22⋊Q8 | semidirect |
| 133. C22×C3 | C22×Q8 | semidirect |
| 146. C23 | C2×Dic6 | semidirect |
| 166. C2×C3 | C2×C22⋊Q8 | semidirect |
| 173. C22 | #878 | direct (N × H) |
| 175. C22 | C22×Dic6 | semidirect |
| 185. C3 | C22×C22⋊Q8 | semidirect |
| 187. C2 | C2×#878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic3 | 2 |
| C23×Dic6 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×#878 | 2 |
| C22×C22⋊Q8 | 3 |