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. #14271506 | C2 | semidirect |
| 4. #14271500 | C2 | semidirect |
| 5. #14271490 | C2 | semidirect |
| 6. #14271478 | C2 | semidirect |
| 7. #14271203 | C2 | semidirect |
| 8. #14271162 | C2 | semidirect |
| 9. #14271160 | C2 | semidirect |
| 10. #14271129 | C2 | semidirect |
| 11. C2×C29×#107 | C2 | semidirect |
| 135. C2×#107 | 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 |
|---|---|
| #14271744 | 2 |
| #14271644 | 2 |
| #14271506 | 2 |
| #14271500 | 2 |
| #14271490 | 2 |
| #14271478 | 2 |
| #14271203 | 2 |
| #14271162 | 2 |
| #14271160 | 2 |
| #14271129 | 2 |
| C2×C29×#107 | 2 |
| #3098 | 29 |