Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C2×#11745225 | C2 | semidirect |
| 4. #14272036 | C2 | semidirect |
| 13. C29×C22⋊Q8 | C4 | semidirect |
| 14. #11745308 | C4 | semidirect |
| 15. #11745286 | C4 | semidirect |
| 16. #11745259 | C4 | semidirect |
| 30. C2×Q8×C29 | C2×C4 | semidirect |
| 44. C2×Dic58 | C2×C4 | semidirect |
| 52. C4⋊C4×C29 | C2×C4 | semidirect |
| 58. C4⋊Dic29 | C2×C4 | semidirect |
| 102. C22×C29 | #103 | semidirect |
| 110. C2×D29 | #103 | semidirect |
| 149. C22⋊Q8 | #1181 | semidirect |
| 159. C29 | #1872 | semidirect |
| 165. C2×Q8 | C2×#1181 | semidirect |
| 192. C4⋊C4 | C2×#1181 | semidirect |
| 249. C22 | #11745225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#1181 | 2 |
| C2×#11745225 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272036 | 2 |
| C22⋊Q8×D29 | 2 |
| #1872 | 29 |