Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272230 | C2 | semidirect |
| 2. #14272161 | C2 | semidirect |
| 3. D29⋊#100 | C2 | semidirect |
| 4. #14272030 | C2 | semidirect |
| 12. C29×#127 | C4 | semidirect |
| 13. #11745302 | C4 | semidirect |
| 16. #11745298 | C4 | semidirect |
| 17. #11745237 | C4 | semidirect |
| 25. C2×D4×C29 | C2×C4 | semidirect |
| 36. C2×Dic58 | C2×C4 | semidirect |
| 41. C4×#1181 | D4 | semidirect |
| 44. C42×C29 | C2×C4 | semidirect |
| 49. C4×Dic29 | C2×C4 | semidirect |
| 112. #127 | #1181 | semidirect |
| 123. C29 | #1911 | semidirect |
| 136. C2×D4 | C2×#1181 | semidirect |
| 152. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272230 | 2 |
| #14272161 | 2 |
| D29⋊#100 | 2 |
| #14272030 | 2 |
| #14271726 | 2 |
| #1911 | 29 |