Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
272 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14272185 | C2 | semidirect |
| 2. #14272099 | C2 | semidirect |
| 3. #14272015 | C2 | semidirect |
| 7. C29×C4⋊Q8 | C4 | semidirect |
| 12. #11745255 | C4 | semidirect |
| 13. #11745236 | C4 | semidirect |
| 89. C4⋊Q8 | #1181 | semidirect |
| 103. C29 | #1505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272185 | 2 |
| #14272099 | 2 |
| #14272015 | 2 |
| #14271714 | 2 |
| #1505 | 29 |