Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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. #14272111 | C2 | semidirect |
| 2. #14272108 | C2 | semidirect |
| 7. C29×#127 | C4 | semidirect |
| 8. #11745302 | C4 | semidirect |
| 9. #11745236 | C4 | semidirect |
| 15. C2×D4×C29 | C2×C4 | semidirect |
| 16. C2×C22⋊D29 | C2×C4 | semidirect |
| 19. C2×D116 | C2×C4 | semidirect |
| 22. C42×C29 | C2×C4 | semidirect |
| 23. C4×Dic29 | C2×C4 | semidirect |
| 58. #127 | #1181 | semidirect |
| 62. C29 | #2380 | semidirect |
| 68. C2×D4 | C2×#1181 | semidirect |
| 74. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272111 | 2 |
| #14272108 | 2 |
| #127×D29 | 2 |
| #2380 | 29 |