Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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. D29⋊#99 | C2 | semidirect |
| 2. #14272069 | C2 | semidirect |
| 3. #14272068 | C2 | semidirect |
| 5. C2×#90809 | C4 | semidirect |
| 8. C29×#124 | C4 | semidirect |
| 10. #11745302 | C4 | semidirect |
| 14. #11745234 | C4 | semidirect |
| 19. C2×Q8×C29 | C2×C4 | semidirect |
| 27. C2×D116 | C2×C4 | semidirect |
| 34. C42×C29 | C2×C4 | semidirect |
| 38. C4×Dic29 | C2×C4 | semidirect |
| 96. #124 | #1181 | semidirect |
| 103. C29 | #2127 | semidirect |
| 106. C2×Q8 | C2×#1181 | semidirect |
| 125. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#99 | 2 |
| #14272069 | 2 |
| #14272068 | 2 |
| #14271731 | 2 |
| #2127 | 29 |