Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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×#92497 | C2 | semidirect |
| 2. C2×#11758489 | C2 | direct (N × H) |
| 3. C22×Dic124 | C2 | semidirect |
| 4. C22×#92480 | C2 | semidirect |
| 5. C22×C8×D31 | C2 | semidirect |
| 6. C22×D8×C31 | C2 | semidirect |
| 11. C2×#92497 | C22 | semidirect |
| 14. C2×D8×C31 | C22 | semidirect |
| 16. C2×#92480 | C22 | semidirect |
| 18. #11758489 | C22 | direct (N × H) |
| 19. C2×Dic124 | C22 | semidirect |
| 20. C2×C8×D31 | C22 | semidirect |
| 31. #92497 | C23 | semidirect |
| 36. D8×C31 | C23 | semidirect |
| 38. #92480 | C23 | semidirect |
| 40. Dic124 | C23 | semidirect |
| 41. C8×D31 | C23 | semidirect |
| 64. C22×C31 | #135 | semidirect |
| 76. C22×D8 | D31 | semidirect |
| 79. C2×C31 | C2×#135 | semidirect |
| 92. C2×D8 | C2×D31 | semidirect |
| 96. C31 | C22×#135 | semidirect |
| 114. D8 | C22×D31 | semidirect |
| 141. C22 | #11758489 | direct (N × H) |
| 149. C2 | C2×#11758489 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92497 | 2 |
| C2×#11758489 | 2 |
| C22×Dic124 | 2 |
| C22×#92480 | 2 |
| C22×C8×D31 | 2 |
| C22×D8×C31 | 2 |
| C22×#135 | 31 |