Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #14271644 | C2 | semidirect |
| 3. #14271502 | C2 | semidirect |
| 4. #14271497 | C2 | semidirect |
| 5. #14271486 | C2 | semidirect |
| 6. #14271475 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. C2×#11745155 | C2 | semidirect |
| 9. #14271159 | C2 | semidirect |
| 10. #14271131 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 136. #417 | D29 | semidirect |
| 174. C29 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271741 | 2 |
| #14271644 | 2 |
| #14271502 | 2 |
| #14271497 | 2 |
| #14271486 | 2 |
| #14271475 | 2 |
| #14271205 | 2 |
| C2×#11745155 | 2 |
| #14271159 | 2 |
| #14271131 | 2 |
| C29×#417 | 2 |
| #3098 | 29 |