Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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. #14272070 | C2 | semidirect |
| 3. #14272069 | C2 | semidirect |
| 5. C2×Q8×D29 | C4 | semidirect |
| 8. C29×#124 | C4 | semidirect |
| 10. #11745298 | C4 | semidirect |
| 14. C42×D29 | C4 | semidirect |
| 19. C2×Q8×C29 | C2×C4 | semidirect |
| 31. C2×Dic58 | C2×C4 | semidirect |
| 35. C42×C29 | C2×C4 | semidirect |
| 40. C4×Dic29 | C2×C4 | semidirect |
| 93. D29 | #354 | semidirect |
| 100. #124 | #1181 | semidirect |
| 106. C29 | C2×#354 | semidirect |
| 112. C2×Q8 | C2×#1181 | semidirect |
| 130. 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 |
| #14272070 | 2 |
| #14272069 | 2 |
| #124×D29 | 2 |
| C2×#354 | 29 |