Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #14272110 | C2 | semidirect |
| 4. #14272040 | C2 | semidirect |
| 19. C29×#99 | C4 | semidirect |
| 20. #11745182 | C4 | semidirect |
| 21. #11745154 | C4 | semidirect |
| 49. C22⋊C4×C29 | C2×C4 | semidirect |
| 50. C22⋊Dic29 | C2×C4 | semidirect |
| 52. C23×C29 | C4⋊C4 | semidirect |
| 60. C22×D29 | C4⋊C4 | semidirect |
| 81. C2×C4×C29 | C4⋊C4 | semidirect |
| 85. C2×Dic29 | C4⋊C4 | semidirect |
| 146. #99 | #1181 | semidirect |
| 149. C29 | #1867 | semidirect |
| 178. C22⋊C4 | C2×#1181 | semidirect |
| 191. C23 | C4⋊#1181 | semidirect |
| 218. C2×C4 | C4⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272230 | 2 |
| #14272111 | 2 |
| #14272110 | 2 |
| #14272040 | 2 |
| #99×D29 | 2 |
| #1867 | 29 |