Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 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. #14271220 | C2 | semidirect |
| 2. #14271029 | C2 | semidirect |
| 3. #14270900 | C2 | semidirect |
| 7. C29×#125 | C4 | semidirect |
| 8. C29×#124 | C4 | semidirect |
| 12. C4×Q8×C29 | C4 | semidirect |
| 14. C4×D4×C29 | C4 | semidirect |
| 104. #125 | Dic29 | semidirect |
| 105. #124 | Dic29 | semidirect |
| 109. C4×Q8 | Dic29 | semidirect |
| 111. C4×D4 | Dic29 | semidirect |
| 120. C29 | #1512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271220 | 2 |
| #14271029 | 2 |
| #14270900 | 2 |
| #14270897 | 2 |
| C29×#529 | 2 |
| #1512 | 29 |