Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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. #14272114 | C2 | semidirect |
| 3. #14272113 | C2 | semidirect |
| 4. #14272106 | C2 | semidirect |
| 5. #14272105 | C2 | semidirect |
| 6. C4×C4⋊#1181 | C2 | semidirect |
| 7. #14272099 | C2 | semidirect |
| 17. C4×D4×C29 | C4 | semidirect |
| 18. D4×Dic29 | C4 | semidirect |
| 19. C4×C22⋊D29 | C4 | semidirect |
| 20. #11745255 | C4 | semidirect |
| 22. #11745243 | C4 | semidirect |
| 24. C4×D116 | C4 | semidirect |
| 148. C4×D4 | #1181 | semidirect |
| 163. C29 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272115 | 2 |
| #14272114 | 2 |
| #14272113 | 2 |
| #14272106 | 2 |
| #14272105 | 2 |
| C4×C4⋊#1181 | 2 |
| #14272099 | 2 |
| C4×D4×D29 | 2 |
| #2319 | 29 |