Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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. #14272194 | C2 | semidirect |
| 2. #14272183 | C2 | semidirect |
| 3. #14272133 | C2 | semidirect |
| 4. C2×C22⋊#6599 | C2 | semidirect |
| 9. C2×#90800 | C22 | semidirect |
| 10. C22×#6599 | C22 | semidirect |
| 18. C22⋊#6599 | C22 | semidirect |
| 19. C22⋊#6599 | C22 | semidirect |
| 20. #11745220 | C22 | semidirect |
| 21. #11745218 | C22 | semidirect |
| 50. C23×C29 | M16 | semidirect |
| 117. C29 | #2973 | semidirect |
| 146. C23 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272194 | 2 |
| #14272183 | 2 |
| #14272133 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×D4×Dic29 | 2 |
| #2973 | 29 |