Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#90785 | C2 | semidirect |
| 5. #14271403 | C2 | direct (N × H) |
| 6. C2×#11745155 | C2 | semidirect |
| 7. C2×#11745164 | C2 | semidirect |
| 8. C2×C29×#103 | C2 | semidirect |
| 17. C2×#90785 | C22 | semidirect |
| 28. C29×#103 | C22 | semidirect |
| 29. #11745164 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 67. C22×D29 | Q16 | semidirect |
| 102. C2×D29 | C2×Q16 | semidirect |
| 118. C2×#103 | D29 | semidirect |
| 119. C2×C29 | #467 | semidirect |
| 145. #103 | C2×D29 | semidirect |
| 146. C29 | C2×#467 | semidirect |
| 227. C2 | #14271403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C22×C8×D29 | 2 |
| C2×#11745259 | 2 |
| C2×#11745308 | 2 |
| #14271403 | 2 |
| C2×#11745155 | 2 |
| C2×#11745164 | 2 |
| C2×C29×#103 | 2 |
| C2×#467 | 29 |