Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 3. C2×#924 | C2 | semidirect |
| 4. #5483 | C2 | direct (N × H) |
| 5. C2×#878 | C2 | semidirect |
| 10. C22×Dic6 | C22 | semidirect |
| 16. C2×C4⋊Dic3 | C22 | semidirect |
| 17. #924 | C22 | semidirect |
| 18. C2×Dic3⋊C4 | C22 | semidirect |
| 19. #878 | C22 | semidirect |
| 26. C24×C3 | Q8 | semidirect |
| 37. C2×Dic6 | C23 | semidirect |
| 41. C4⋊Dic3 | C23 | semidirect |
| 42. Dic3⋊C4 | C23 | semidirect |
| 62. C23×C3 | C2×Q8 | semidirect |
| 74. C24 | Dic6 | semidirect |
| 109. C23 | C2×Dic6 | semidirect |
| 122. C2×C3 | #543 | semidirect |
| 137. C3 | C2×#543 | semidirect |
| 140. C2 | #5483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C2×#924 | 2 |
| #5483 | 2 |
| C2×#878 | 2 |
| C2×#543 | 3 |