Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #14271127 | C2 | semidirect |
| 2. C4×C22⋊Dic29 | C2 | semidirect |
| 3. #14270897 | C2 | semidirect |
| 6. C22×D4×C29 | C4 | semidirect |
| 10. C29×#121 | C4 | semidirect |
| 12. C2×C4⋊C4×C29 | C4 | semidirect |
| 17. #11745179 | C22 | semidirect |
| 19. C22⋊#6597 | C22 | semidirect |
| 109. C22×D4 | Dic29 | semidirect |
| 114. #121 | Dic29 | semidirect |
| 116. C2×C4⋊C4 | Dic29 | semidirect |
| 123. C29 | #1507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271127 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14270897 | 2 |
| C2×C29×#121 | 2 |
| #1507 | 29 |