Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271929 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. #14271179 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 19. #11745237 | C4 | semidirect |
| 20. #11745237 | C4 | semidirect |
| 21. #11745236 | C4 | semidirect |
| 23. #11745231 | C4 | semidirect |
| 47. M16×C29 | D4 | semidirect |
| 62. #90777 | D4 | semidirect |
| 126. #339 | D29 | semidirect |
| 152. C29 | #1884 | semidirect |
| 176. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271929 | 2 |
| #14271713 | 2 |
| #14271181 | 2 |
| #14271179 | 2 |
| #14271136 | 2 |
| #14270923 | 2 |
| C29×#339 | 2 |
| #1884 | 29 |