Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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×Dic58 | C2 | semidirect |
| 3. C2×#11745259 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic29 | C2 | semidirect |
| 6. C22×C4⋊C4×C29 | C2 | semidirect |
| 15. C22×Dic58 | C22 | semidirect |
| 16. C2×C4⋊C4×C29 | C22 | semidirect |
| 18. C2×C4⋊Dic29 | C22 | semidirect |
| 19. #11745259 | C22 | direct (N × H) |
| 23. C23×D29 | Q8 | semidirect |
| 36. C2×Dic58 | C23 | semidirect |
| 37. C4⋊C4×C29 | C23 | semidirect |
| 39. C4⋊Dic29 | C23 | semidirect |
| 47. C22×D29 | C2×Q8 | semidirect |
| 60. C22×C29 | C22⋊Q8 | semidirect |
| 68. C2×D29 | C22×Q8 | semidirect |
| 77. C22×C4⋊C4 | D29 | semidirect |
| 79. C2×C29 | C2×C22⋊Q8 | semidirect |
| 95. C2×C4⋊C4 | C2×D29 | semidirect |
| 97. C29 | C22×C22⋊Q8 | semidirect |
| 116. C4⋊C4 | C22×D29 | semidirect |
| 141. C22 | #11745259 | direct (N × H) |
| 151. C2 | C2×#11745259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C23×C4×D29 | 2 |
| C2×#11745259 | 2 |
| C22×C4⋊Dic29 | 2 |
| C22×#90781 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C22×C22⋊Q8 | 29 |