Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 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. D29⋊(C4⋊C8) | C2 | semidirect |
| 2. C2×#11745225 | C2 | semidirect |
| 4. C4×C4⋊#1181 | C2 | semidirect |
| 11. C29×#124 | C4 | semidirect |
| 12. #11745309 | C4 | semidirect |
| 13. #11745298 | C4 | semidirect |
| 18. #11745237 | C4 | semidirect |
| 136. #124 | #1181 | semidirect |
| 147. C29 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊(C4⋊C8) | 2 |
| C2×#11745225 | 2 |
| C2×#11745223 | 2 |
| C4×C4⋊#1181 | 2 |
| #124×D29 | 2 |
| #1983 | 29 |