Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14272135 | C2 | semidirect |
| 2. #14272106 | C2 | semidirect |
| 3. #14272014 | C2 | semidirect |
| 5. C22×D4×C29 | C4 | semidirect |
| 13. #11745300 | C4 | semidirect |
| 15. C2×C4⋊Dic29 | C4 | semidirect |
| 17. (C2×#1181)⋊C4 | C22 | semidirect |
| 19. #11745219 | C22 | semidirect |
| 108. C22×D4 | #1181 | semidirect |
| 122. C29 | #1510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272135 | 2 |
| #14272106 | 2 |
| #14272014 | 2 |
| C2×#11745300 | 2 |
| #1510 | 29 |