Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #14521605 | C2 | direct (N × H) |
| 2. C2×#11758465 | C2 | semidirect |
| 3. C2×#11758447 | C2 | semidirect |
| 5. C2×#11758464 | C2 | semidirect |
| 8. C2×C31×#125 | C2 | semidirect |
| 12. C31×#125 | C22 | semidirect |
| 25. #11758465 | C22 | semidirect |
| 26. #11758464 | C22 | semidirect |
| 28. #11758447 | C22 | semidirect |
| 37. C2×C4×D31 | Q8 | semidirect |
| 69. C4×D31 | C2×Q8 | semidirect |
| 87. C2×#125 | D31 | semidirect |
| 92. C2×C31 | #533 | semidirect |
| 101. #125 | C2×D31 | semidirect |
| 116. C31 | C2×#533 | semidirect |
| 172. C2 | #14521605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521605 | 2 |
| C2×#11758465 | 2 |
| C2×#11758447 | 2 |
| C2×#11758473 | 2 |
| C2×#11758464 | 2 |
| C2×#11758469 | 2 |
| C2×C42×D31 | 2 |
| C2×C31×#125 | 2 |
| C2×#533 | 31 |