Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D29 | C2 | semidirect |
| 3. #14271478 | C2 | semidirect |
| 4. #14271455 | C2 | semidirect |
| 5. #14271364 | C2 | semidirect |
| 6. #14271363 | C2 | semidirect |
| 7. #14271303 | C2 | semidirect |
| 8. #14271266 | C2 | semidirect |
| 9. #14271262 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#477 | C2 | semidirect |
| 87. Q8×C29 | #41 | semidirect |
| 113. Dic58 | #41 | semidirect |
| 140. #477 | D29 | semidirect |
| 183. C29 | #3112 | semidirect |
| 231. Q8 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| C4×Q8×D29 | 2 |
| #14271478 | 2 |
| #14271455 | 2 |
| #14271364 | 2 |
| #14271363 | 2 |
| #14271303 | 2 |
| #14271266 | 2 |
| #14271262 | 2 |
| #14271219 | 2 |
| C29×#477 | 2 |
| #3112 | 29 |