Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271720 | C2 | semidirect |
| 3. #14271523 | C2 | semidirect |
| 4. #14271518 | C2 | semidirect |
| 5. #14271173 | C2 | semidirect |
| 7. C4×M16×C29 | C2 | semidirect |
| 18. #11745232 | C22 | semidirect |
| 19. #11745231 | C22 | semidirect |
| 21. C29×#97 | C22 | semidirect |
| 22. C4×C8×C29 | C22 | semidirect |
| 24. #11745164 | C22 | semidirect |
| 86. C4×M16 | D29 | semidirect |
| 106. #97 | C2×D29 | semidirect |
| 107. C4×C8 | C2×D29 | semidirect |
| 108. C29 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| C2×#11745237 | 2 |
| #14271523 | 2 |
| #14271518 | 2 |
| #14271173 | 2 |
| #14271169 | 2 |
| C4×M16×C29 | 2 |
| #3140 | 29 |