Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#11745210 | C2 | semidirect |
| 2. C2×#11745209 | C2 | semidirect |
| 4. #14272037 | C2 | semidirect |
| 10. C2×M16×C29 | C4 | semidirect |
| 11. C2×#90777 | C4 | semidirect |
| 14. C2×#90772 | C4 | semidirect |
| 15. C2×#90772 | C4 | semidirect |
| 83. C8×C29 | C22⋊C4 | semidirect |
| 85. #6597 | C22⋊C4 | semidirect |
| 125. C2×M16 | #1181 | semidirect |
| 134. C29 | #1809 | semidirect |
| 199. C8 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745210 | 2 |
| C2×#11745209 | 2 |
| #14272105 | 2 |
| #14272037 | 2 |
| C2×M16×D29 | 2 |
| #1809 | 29 |