Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1664 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 981 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 |
|---|---|---|
| 6. C2×C4×Dic6 | C2 | direct (N × H) |
| 13. C22×Dic6 | C4 | direct (N × H) |
| 19. C4×Dic6 | C22 | direct (N × H) |
| 29. C22×C3×C4 | Q8 | semidirect |
| 37. C2×Dic6 | C2×C4 | direct (N × H) |
| 61. C2×C3×C4 | C2×Q8 | semidirect |
| 69. Dic6 | C22×C4 | direct (N × H) |
| 78. C22×C4 | Dic6 | direct (N × H) |
| 87. C22×C3 | C4×Q8 | semidirect |
| 94. C3×C4 | C22×Q8 | semidirect |
| 107. C2×C4 | C2×Dic6 | direct (N × H) |
| 112. C2×C3 | C2×C4×Q8 | semidirect |
| 116. C22 | C4×Dic6 | direct (N × H) |
| 124. C4 | C22×Dic6 | direct (N × H) |
| 126. C3 | C22×C4×Q8 | semidirect |
| 127. C2 | C2×C4×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×C3×C42 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×C4×Dic6 | 2 |
| C22×C4×Q8 | 3 |