Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 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. C2×#11745209 | C2 | semidirect |
| 2. C2×#11745223 | C2 | semidirect |
| 3. C2×#11745208 | C2 | semidirect |
| 4. #14272115 | C2 | semidirect |
| 11. C2×D8×C29 | C4 | semidirect |
| 12. C2×#90782 | C4 | semidirect |
| 15. C2×D232 | C4 | semidirect |
| 70. C8×C29 | C22⋊C4 | semidirect |
| 71. #6597 | C22⋊C4 | semidirect |
| 106. C2×D8 | #1181 | semidirect |
| 115. C29 | #1972 | semidirect |
| 167. C8 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745209 | 2 |
| C2×#11745223 | 2 |
| C2×#11745208 | 2 |
| #14272115 | 2 |
| C2×D8×D29 | 2 |
| #1972 | 29 |