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×#11758492 | C2 | direct (N × H) |
| 4. C22×Dic124 | C2 | semidirect |
| 5. C22×#92482 | C2 | semidirect |
| 6. C22×#92480 | C2 | semidirect |
| 7. C22×#92469 | C2 | semidirect |
| 8. C22×SD16×C31 | C2 | semidirect |
| 14. C2×Q8×D31 | C22 | semidirect |
| 22. C2×SD16×C31 | C22 | semidirect |
| 24. C2×#92482 | C22 | semidirect |
| 25. C2×#92480 | C22 | semidirect |
| 27. #11758492 | C22 | direct (N × H) |
| 28. C2×Dic124 | C22 | semidirect |
| 29. C2×#92469 | C22 | semidirect |
| 44. Q8×D31 | C23 | semidirect |
| 55. SD16×C31 | C23 | semidirect |
| 57. #92482 | C23 | semidirect |
| 58. #92480 | C23 | semidirect |
| 60. Dic124 | C23 | semidirect |
| 61. #92469 | C23 | semidirect |
| 92. C22×C31 | #137 | semidirect |
| 108. C22×SD16 | D31 | semidirect |
| 111. C2×C31 | C2×#137 | semidirect |
| 131. C2×SD16 | C2×D31 | semidirect |
| 135. C31 | C22×#137 | semidirect |
| 164. SD16 | C22×D31 | semidirect |
| 199. C22 | #11758492 | direct (N × H) |
| 209. C2 | C2×#11758492 | 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 |
| C22×Q8×D31 | 2 |
| C2×#11758492 | 2 |
| C22×Dic124 | 2 |
| C22×#92482 | 2 |
| C22×#92480 | 2 |
| C22×#92469 | 2 |
| C22×SD16×C31 | 2 |
| C22×#137 | 31 |