Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 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. #14272214 | C2 | semidirect |
| 2. #14272194 | C2 | semidirect |
| 3. D4×#6599 | C2 | semidirect |
| 4. #14272183 | C2 | semidirect |
| 5. #14272180 | C2 | semidirect |
| 6. #14272166 | C2 | semidirect |
| 7. C2×#11745220 | C2 | semidirect |
| 64. D4×C29 | M16 | semidirect |
| 138. C29 | #2990 | semidirect |
| 172. D4 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| #14272194 | 2 |
| D4×#6599 | 2 |
| #14272183 | 2 |
| #14272180 | 2 |
| #14272166 | 2 |
| C2×#11745220 | 2 |
| #41×Dic29 | 2 |
| #2990 | 29 |