Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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. #14271501 | C2 | semidirect |
| 3. #14271460 | C2 | semidirect |
| 4. #14271365 | C2 | semidirect |
| 6. #14271261 | C2 | semidirect |
| 7. C4×#90784 | C2 | semidirect |
| 8. #14271224 | C2 | semidirect |
| 9. C29×#541 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 14. C29×#125 | C22 | semidirect |
| 16. C4×Q8×C29 | C22 | semidirect |
| 25. #11745183 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 31. #11745155 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 33. #11745151 | C22 | semidirect |
| 34. C4×#6597 | C22 | semidirect |
| 99. #541 | D29 | semidirect |
| 115. C4⋊Q8 | C2×D29 | semidirect |
| 118. #125 | C2×D29 | semidirect |
| 120. C4×Q8 | C2×D29 | semidirect |
| 137. C29 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271637 | 2 |
| #14271501 | 2 |
| #14271460 | 2 |
| #14271365 | 2 |
| #14271313 | 2 |
| #14271261 | 2 |
| C4×#90784 | 2 |
| #14271224 | 2 |
| C29×#541 | 2 |
| #3123 | 29 |