Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4⋊C4×D29 | C2 | semidirect |
| 3. #14271497 | C2 | semidirect |
| 4. #14271492 | C2 | semidirect |
| 5. #14271480 | C2 | semidirect |
| 6. #14271475 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. #14271203 | C2 | semidirect |
| 9. #14271164 | C2 | semidirect |
| 10. #14271126 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 33. C29×#103 | C22 | semidirect |
| 34. C29×#102 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 39. #11745166 | C22 | semidirect |
| 40. #11745165 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 158. #417 | D29 | semidirect |
| 193. #103 | C2×D29 | semidirect |
| 195. #102 | C2×D29 | semidirect |
| 198. C29 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271670 | 2 |
| C2×C4⋊C4×D29 | 2 |
| #14271497 | 2 |
| #14271492 | 2 |
| #14271480 | 2 |
| #14271475 | 2 |
| #14271205 | 2 |
| #14271203 | 2 |
| #14271164 | 2 |
| #14271126 | 2 |
| C29×#417 | 2 |
| #3092 | 29 |