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×#92499 | C2 | semidirect |
| 2. C22×#92497 | C2 | semidirect |
| 3. C2×#11758493 | C2 | direct (N × H) |
| 4. C22×#92482 | C2 | semidirect |
| 5. C22×#92470 | C2 | semidirect |
| 6. C22×#92479 | C2 | semidirect |
| 7. C22×C8×D31 | C2 | semidirect |
| 8. C22×SD16×C31 | C2 | semidirect |
| 14. C2×#92499 | C22 | semidirect |
| 16. C2×#92497 | C22 | semidirect |
| 22. C2×SD16×C31 | C22 | semidirect |
| 24. C2×#92482 | C22 | semidirect |
| 25. C2×#92479 | C22 | semidirect |
| 27. #11758493 | C22 | direct (N × H) |
| 28. C2×#92470 | C22 | semidirect |
| 29. C2×C8×D31 | C22 | semidirect |
| 44. #92499 | C23 | semidirect |
| 46. #92497 | C23 | semidirect |
| 55. SD16×C31 | C23 | semidirect |
| 57. #92482 | C23 | semidirect |
| 58. #92479 | C23 | semidirect |
| 60. #92470 | C23 | semidirect |
| 61. C8×D31 | C23 | semidirect |
| 93. C22×C31 | #135 | semidirect |
| 109. C22×SD16 | D31 | semidirect |
| 113. C2×C31 | C2×#135 | semidirect |
| 133. C2×SD16 | C2×D31 | semidirect |
| 138. C31 | C22×#135 | semidirect |
| 166. SD16 | C22×D31 | semidirect |
| 205. C22 | #11758493 | direct (N × H) |
| 215. C2 | C2×#11758493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92499 | 2 |
| C22×#92497 | 2 |
| C2×#11758493 | 2 |
| C22×#92482 | 2 |
| C22×#92470 | 2 |
| C22×#92479 | 2 |
| C22×C8×D31 | 2 |
| C22×SD16×C31 | 2 |
| C22×#135 | 31 |