Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
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×#92495 | C2 | semidirect |
| 2. C2×#11758527 | C2 | direct (N × H) |
| 3. C22×#92482 | C2 | semidirect |
| 4. C22×#92480 | C2 | semidirect |
| 5. C22×#92481 | C2 | semidirect |
| 6. C22×#92479 | C2 | semidirect |
| 7. C23×C31⋊C8 | C2 | semidirect |
| 8. C22×#41×C31 | C2 | semidirect |
| 10. C2×#41×C31 | C22 | semidirect |
| 18. C2×#92495 | C22 | semidirect |
| 22. #11758527 | C22 | direct (N × H) |
| 23. C2×#92482 | C22 | semidirect |
| 24. C2×#92481 | C22 | semidirect |
| 25. C2×#92480 | C22 | semidirect |
| 26. C2×#92479 | C22 | semidirect |
| 29. C22×C31⋊C8 | C22 | semidirect |
| 34. #41×C31 | C23 | semidirect |
| 49. #92495 | C23 | semidirect |
| 55. #92482 | C23 | semidirect |
| 56. #92481 | C23 | semidirect |
| 57. #92480 | C23 | semidirect |
| 58. #92479 | C23 | semidirect |
| 61. C2×C31⋊C8 | C23 | semidirect |
| 94. C22×C31 | #135 | semidirect |
| 105. C22×#41 | D31 | semidirect |
| 114. C2×C31 | C2×#135 | semidirect |
| 120. C2×#41 | C2×D31 | semidirect |
| 138. C31 | C22×#135 | semidirect |
| 145. #41 | C22×D31 | semidirect |
| 204. C22 | #11758527 | direct (N × H) |
| 215. C2 | C2×#11758527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92495 | 2 |
| C2×#11758527 | 2 |
| C22×#92482 | 2 |
| C22×#92480 | 2 |
| C22×#92481 | 2 |
| C22×#92479 | 2 |
| C23×C31⋊C8 | 2 |
| C22×#41×C31 | 2 |
| C22×#135 | 31 |