Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14272181 | C2 | semidirect |
| 2. D29⋊(C4⋊C8) | C2 | semidirect |
| 3. Q8⋊#6599 | C2 | semidirect |
| 4. #14272011 | C2 | semidirect |
| 25. #90809 | C8 | semidirect |
| 54. Q8×C29 | C2×C8 | semidirect |
| 66. D116 | C2×C8 | semidirect |
| 124. C29 | #1477 | semidirect |
| 156. Q8 | D29⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272181 | 2 |
| D29⋊(C4⋊C8) | 2 |
| Q8⋊#6599 | 2 |
| #14272011 | 2 |
| C4×#90809 | 2 |
| #1477 | 29 |