Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C4⋊C4×D31 | C2 | semidirect |
| 3. #14521369 | C2 | direct (N × H) |
| 4. C2×#11758396 | C2 | semidirect |
| 5. C2×#11758409 | C2 | semidirect |
| 6. C2×#11758397 | C2 | semidirect |
| 7. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 8. C2×C31×#106 | C2 | semidirect |
| 23. C4⋊C4×D31 | C22 | semidirect |
| 24. C31×#106 | C22 | semidirect |
| 25. #11758409 | C22 | semidirect |
| 26. (C2×D31)⋊C8 | C22 | semidirect |
| 27. #11758397 | C22 | semidirect |
| 28. #11758396 | C22 | semidirect |
| 115. C2×#106 | D31 | semidirect |
| 119. C2×C31 | #481 | semidirect |
| 141. #106 | C2×D31 | semidirect |
| 145. C31 | C2×#481 | semidirect |
| 229. C2 | #14521369 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758472 | 2 |
| C2×C4⋊C4×D31 | 2 |
| #14521369 | 2 |
| C2×#11758396 | 2 |
| C2×#11758409 | 2 |
| C2×#11758397 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C2×C31×#106 | 2 |
| C2×#481 | 31 |