Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 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 |
|---|---|---|
| 2. C22×Q8×D31 | C2 | semidirect |
| 3. C2×#11758495 | C2 | direct (N × H) |
| 4. C22×#92482 | C2 | semidirect |
| 5. C22×#92470 | C2 | semidirect |
| 6. C22×#92481 | C2 | semidirect |
| 7. C22×#92469 | C2 | semidirect |
| 8. C22×Q16×C31 | C2 | semidirect |
| 14. C2×Q8×D31 | C22 | semidirect |
| 22. C2×Q16×C31 | C22 | semidirect |
| 24. C2×#92482 | C22 | semidirect |
| 25. C2×#92481 | C22 | semidirect |
| 27. #11758495 | C22 | direct (N × H) |
| 28. C2×#92470 | C22 | semidirect |
| 29. C2×#92469 | C22 | semidirect |
| 44. Q8×D31 | C23 | semidirect |
| 55. Q16×C31 | C23 | semidirect |
| 57. #92482 | C23 | semidirect |
| 58. #92481 | C23 | semidirect |
| 60. #92470 | C23 | semidirect |
| 61. #92469 | C23 | semidirect |
| 90. C22×C31 | #137 | semidirect |
| 106. C22×Q16 | D31 | semidirect |
| 110. C2×C31 | C2×#137 | semidirect |
| 129. C2×Q16 | C2×D31 | semidirect |
| 135. C31 | C22×#137 | semidirect |
| 162. Q16 | C22×D31 | semidirect |
| 199. C22 | #11758495 | direct (N × H) |
| 209. C2 | C2×#11758495 | 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×Q8×D31 | 2 |
| C2×#11758495 | 2 |
| C22×#92482 | 2 |
| C22×#92470 | 2 |
| C22×#92481 | 2 |
| C22×#92469 | 2 |
| C22×Q16×C31 | 2 |
| C22×#137 | 31 |