Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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. C2×#11745263 | C2 | semidirect |
| 3. #14271286 | C2 | semidirect |
| 4. #14271281 | C2 | semidirect |
| 5. #14271212 | C2 | semidirect |
| 6. #14271181 | C2 | semidirect |
| 7. C29×#405 | C2 | semidirect |
| 13. #11745271 | C4 | semidirect |
| 14. #11745270 | C4 | semidirect |
| 18. #11745263 | C22 | semidirect |
| 19. #11745263 | C22 | semidirect |
| 22. C29×#97 | C22 | semidirect |
| 23. C4×C8×C29 | C22 | semidirect |
| 24. #11745167 | C22 | semidirect |
| 25. #11745153 | C22 | semidirect |
| 92. #405 | D29 | semidirect |
| 113. #97 | C2×D29 | semidirect |
| 114. C4×C8 | C2×D29 | semidirect |
| 115. C29 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| C2×#11745263 | 2 |
| #14271286 | 2 |
| #14271281 | 2 |
| #14271212 | 2 |
| #14271181 | 2 |
| C29×#405 | 2 |
| #2955 | 29 |