Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
848 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 104 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×#11745223 | C2 | semidirect |
| 2. D29⋊(C22⋊C8) | C2 | semidirect |
| 3. #14272105 | C2 | semidirect |
| 6. C22×D4×C29 | C4 | semidirect |
| 11. C2×D4×D29 | C4 | semidirect |
| 13. C22×D116 | C4 | semidirect |
| 16. C2×C4⋊#1181 | C22 | semidirect |
| 17. C2×D29⋊C8 | C22 | semidirect |
| 87. D4×C29 | C22⋊C4 | semidirect |
| 98. D116 | C22⋊C4 | semidirect |
| 111. C22×C29 | #102 | semidirect |
| 124. C2×D29 | #102 | semidirect |
| 155. C22×D4 | #1181 | semidirect |
| 164. C29 | #1786 | semidirect |
| 232. D4 | C22⋊#1181 | semidirect |
| 269. C22 | #11745223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745223 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272105 | 2 |
| C22×D4×D29 | 2 |
| #1786 | 29 |