Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×#897 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4776 | C2 | direct (N × H) |
| 19. C22×Dic6 | C22 | semidirect |
| 20. C22×C3×C8 | C22 | semidirect |
| 21. C2×C3×C4⋊C4 | C22 | semidirect |
| 23. C2×#214 | C22 | semidirect |
| 26. C22×C3⋊C8 | C22 | semidirect |
| 28. C2×#204 | C22 | semidirect |
| 30. #897 | C22 | semidirect |
| 31. C3×#102 | C22 | semidirect |
| 32. (C2×D3)⋊C8 | C22 | semidirect |
| 33. #809 | C22 | semidirect |
| 40. C2×#102 | D3 | semidirect |
| 73. C2×Dic6 | C23 | semidirect |
| 75. C2×C3×C8 | C23 | semidirect |
| 77. C3×C4⋊C4 | C23 | semidirect |
| 82. C2×C3⋊C8 | C23 | semidirect |
| 99. C22×C8 | C2×D3 | semidirect |
| 103. C2×C4⋊C4 | C2×D3 | semidirect |
| 106. #102 | C2×D3 | semidirect |
| 123. C22×D3 | SD16 | semidirect |
| 187. C2×C8 | C22×D3 | semidirect |
| 190. C4⋊C4 | C22×D3 | semidirect |
| 208. C2×D3 | C2×SD16 | semidirect |
| 258. C2×C3 | #450 | semidirect |
| 287. C3 | C2×#450 | semidirect |
| 291. C2 | #4776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D4 | 2 |
| C22×#214 | 2 |
| C22×#204 | 2 |
| C2×#897 | 2 |
| C2×C3×#102 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#809 | 2 |
| #4776 | 2 |
| C2×#450 | 3 |