Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 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. C22×#90768 | C2 | semidirect |
| 2. C4⋊#90768 | C2 | semidirect |
| 3. C22⋊#90768 | C2 | semidirect |
| 4. C4×#90768 | C2 | semidirect |
| 27. #90768 | D4 | direct (N × H) |
| 29. D4×C29 | C16 | semidirect |
| 43. C22×C29 | C2×C16 | semidirect |
| 47. C4×C29 | C2×C16 | semidirect |
| 68. C29 | D4×C16 | semidirect |
| 83. D4 | #90768 | direct (N × H) |
| 96. C22 | C2×#90768 | semidirect |
| 100. C4 | C2×#90768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90768 | 2 |
| C4⋊#90768 | 2 |
| C22⋊#90768 | 2 |
| C4×#90768 | 2 |
| C8×D4×C29 | 2 |
| D4×C16 | 29 |