Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×D4×Dic3 | C2 | semidirect |
| 3. C2×#893 | C2 | semidirect |
| 4. C2×C3×#102 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. C2×#815 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4785 | C2 | direct (N × H) |
| 18. D4×Dic3 | C22 | semidirect |
| 19. C2×#213 | C4 | semidirect |
| 26. #893 | C22 | semidirect |
| 27. C3×#102 | C22 | semidirect |
| 28. #821 | C22 | semidirect |
| 29. #815 | C22 | semidirect |
| 30. #808 | C22 | semidirect |
| 37. C2×#102 | D3 | semidirect |
| 43. C2×C3×D4 | C2×C4 | semidirect |
| 54. C2×D12 | C2×C4 | semidirect |
| 63. #213 | C2×C4 | semidirect |
| 69. C2×C3⋊C8 | C2×C4 | semidirect |
| 90. #102 | C2×D3 | semidirect |
| 103. C3×D4 | C22×C4 | semidirect |
| 119. D12 | C22×C4 | semidirect |
| 122. C3⋊C8 | C22×C4 | semidirect |
| 131. C2×D4 | C4×D3 | semidirect |
| 188. D4 | C2×C4×D3 | semidirect |
| 206. C2×C3 | #442 | semidirect |
| 230. C3 | C2×#442 | semidirect |
| 233. C2 | #4785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C22×#213 | 2 |
| C2×#893 | 2 |
| C2×C3×#102 | 2 |
| C2×#821 | 2 |
| C2×#815 | 2 |
| C2×#808 | 2 |
| #4785 | 2 |
| C2×#442 | 3 |