Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745281 | C2 | semidirect |
| 2. C22×C8×D29 | C2 | semidirect |
| 3. #14271676 | C2 | semidirect |
| 4. #14271401 | C2 | semidirect |
| 5. #14271400 | C2 | semidirect |
| 6. #14271399 | C2 | semidirect |
| 7. #14271395 | C2 | semidirect |
| 8. #14271394 | C2 | semidirect |
| 9. #14271200 | C2 | semidirect |
| 10. #14271158 | C2 | semidirect |
| 11. C29×#467 | C2 | semidirect |
| 14. C2×Q16×C29 | C22 | semidirect |
| 18. C2×#90784 | C22 | semidirect |
| 22. C2×D232 | C22 | semidirect |
| 34. C29×#107 | C22 | semidirect |
| 35. C29×#103 | C22 | semidirect |
| 36. #11745183 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745166 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745156 | C22 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 119. C22×C29 | #135 | semidirect |
| 130. C2×D29 | #135 | semidirect |
| 143. #467 | D29 | semidirect |
| 160. C2×Q16 | C2×D29 | semidirect |
| 180. #107 | C2×D29 | semidirect |
| 183. #103 | C2×D29 | semidirect |
| 186. C29 | #3050 | semidirect |
| 274. C22 | #11745281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C22×C8×D29 | 2 |
| #14271676 | 2 |
| #14271401 | 2 |
| #14271400 | 2 |
| #14271399 | 2 |
| #14271395 | 2 |
| #14271394 | 2 |
| #14271200 | 2 |
| #14271158 | 2 |
| C29×#467 | 2 |
| #3050 | 29 |