Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #14272184 | C2 | semidirect |
| 2. C4×#90800 | C2 | semidirect |
| 3. D4⋊#6599 | C2 | semidirect |
| 18. C4⋊#6599 | C22 | semidirect |
| 19. C4×#6599 | C22 | semidirect |
| 49. D4×C29 | M16 | semidirect |
| 105. C29 | #1490 | semidirect |
| 135. D4 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272184 | 2 |
| C4×#90800 | 2 |
| D4⋊#6599 | 2 |
| C2×D4×Dic29 | 2 |
| #1490 | 29 |