Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1840 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×Dic62 | C2 | semidirect |
| 3. C2×#11758473 | C2 | direct (N × H) |
| 4. C22×Dic31⋊C4 | C2 | semidirect |
| 5. C22×Dic31⋊C4 | C2 | semidirect |
| 8. C22×C4⋊C4×C31 | C2 | semidirect |
| 19. C22×Dic62 | C22 | semidirect |
| 20. C2×C4⋊C4×C31 | C22 | semidirect |
| 23. C2×Dic31⋊C4 | C22 | semidirect |
| 24. C2×Dic31⋊C4 | C22 | semidirect |
| 25. #11758473 | C22 | direct (N × H) |
| 29. C23×D31 | Q8 | semidirect |
| 46. C2×Dic62 | C23 | semidirect |
| 47. C4⋊C4×C31 | C23 | semidirect |
| 50. Dic31⋊C4 | C23 | semidirect |
| 51. Dic31⋊C4 | C23 | semidirect |
| 59. C22×D31 | C2×Q8 | semidirect |
| 76. C22×C31 | C22⋊Q8 | semidirect |
| 84. C2×D31 | C22×Q8 | semidirect |
| 96. C22×C4⋊C4 | D31 | semidirect |
| 99. C2×C31 | C2×C22⋊Q8 | semidirect |
| 118. C2×C4⋊C4 | C2×D31 | semidirect |
| 121. C31 | C22×C22⋊Q8 | semidirect |
| 145. C4⋊C4 | C22×D31 | semidirect |
| 175. C22 | #11758473 | direct (N × H) |
| 187. C2 | C2×#11758473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic62 | 2 |
| C23×C4×D31 | 2 |
| C2×#11758473 | 2 |
| C22×Dic31⋊C4 | 2 |
| C22×(C2×D31)⋊C4 | 2 |
| C22×C4⋊C4×C31 | 2 |
| C22×C22⋊Q8 | 31 |