Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 344 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. #14272241 | C2 | semidirect |
| 2. #14272155 | C2 | semidirect |
| 3. #14272143 | C2 | semidirect |
| 4. #14272030 | C2 | semidirect |
| 12. C29×#127 | C4 | semidirect |
| 13. #11745302 | C4 | semidirect |
| 16. #11745298 | C4 | semidirect |
| 17. #11745237 | C4 | semidirect |
| 43. D29⋊C8 | D4 | semidirect |
| 111. #127 | #1181 | semidirect |
| 120. C29 | #1910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272241 | 2 |
| #14272155 | 2 |
| #14272143 | 2 |
| #14272030 | 2 |
| #14271726 | 2 |
| #1910 | 29 |