Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 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 |
|---|---|---|
| 1. C22×C3×#41 | C2 | semidirect |
| 2. C22×#235 | C2 | semidirect |
| 3. C2×#950 | C2 | direct (N × H) |
| 4. C22×#216 | C2 | semidirect |
| 5. C22×#215 | C2 | semidirect |
| 6. C22×#214 | C2 | semidirect |
| 7. C22×#213 | C2 | semidirect |
| 8. C23×C3⋊C8 | C2 | semidirect |
| 11. C2×C3×#41 | C22 | semidirect |
| 19. C2×#235 | C22 | semidirect |
| 23. #950 | C22 | direct (N × H) |
| 24. C2×#216 | C22 | semidirect |
| 25. C2×#215 | C22 | semidirect |
| 26. C2×#214 | C22 | semidirect |
| 27. C2×#213 | C22 | semidirect |
| 30. C22×C3⋊C8 | C22 | semidirect |
| 32. C22×#41 | D3 | semidirect |
| 43. C3×#41 | C23 | semidirect |
| 58. #235 | C23 | semidirect |
| 64. #216 | C23 | semidirect |
| 65. #215 | C23 | semidirect |
| 66. #214 | C23 | semidirect |
| 67. #213 | C23 | semidirect |
| 70. C2×C3⋊C8 | C23 | semidirect |
| 74. C2×#41 | C2×D3 | semidirect |
| 126. #41 | C22×D3 | semidirect |
| 155. C22×C3 | #135 | semidirect |
| 195. C2×C3 | C2×#135 | semidirect |
| 203. C22 | #950 | direct (N × H) |
| 211. C3 | C22×#135 | semidirect |
| 215. C2 | C2×#950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C22×#235 | 2 |
| C2×#950 | 2 |
| C22×#216 | 2 |
| C22×#215 | 2 |
| C22×#214 | 2 |
| C22×#213 | 2 |
| C23×C3⋊C8 | 2 |
| C22×#135 | 3 |