Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 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. #14271598 | C2 | semidirect |
| 2. #14271538 | C2 | semidirect |
| 3. #14271280 | C2 | semidirect |
| 4. #14270983 | C2 | semidirect |
| 5. #14270977 | C2 | semidirect |
| 6. #14270976 | C2 | semidirect |
| 7. C29×#509 | C2 | semidirect |
| 27. Q16×C29 | D4 | semidirect |
| 31. D8×C29 | D4 | semidirect |
| 74. #509 | D29 | semidirect |
| 100. C29 | #2213 | semidirect |
| 105. Q16 | C22⋊D29 | semidirect |
| 113. D8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271598 | 2 |
| #14271538 | 2 |
| #14271280 | 2 |
| #14270983 | 2 |
| #14270977 | 2 |
| #14270976 | 2 |
| C29×#509 | 2 |
| #2213 | 29 |