Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#90773 | C2 | semidirect |
| 2. #14271734 | C2 | semidirect |
| 4. #14271409 | C2 | semidirect |
| 5. #14271392 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 8. #14271169 | C2 | semidirect |
| 9. C2×C29×#131 | C2 | semidirect |
| 15. C2×M16×C29 | C22 | semidirect |
| 17. C22×C8×C29 | C22 | semidirect |
| 27. #11745286 | C22 | semidirect |
| 32. #11745166 | C22 | semidirect |
| 33. #11745165 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 56. C2×C8×C29 | D4 | semidirect |
| 117. C2×#131 | D29 | semidirect |
| 138. C2×M16 | C2×D29 | semidirect |
| 140. C22×C8 | C2×D29 | semidirect |
| 155. C29 | #3057 | semidirect |
| 179. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| #14271734 | 2 |
| #14271727 | 2 |
| #14271409 | 2 |
| #14271392 | 2 |
| #14271201 | 2 |
| #14271173 | 2 |
| #14271169 | 2 |
| C2×C29×#131 | 2 |
| #3057 | 29 |