Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4⋊Dic29 | C2 | semidirect |
| 3. #14271165 | C2 | direct (N × H) |
| 4. C2×#11745164 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C22×M16×C29 | C2 | semidirect |
| 12. C2×#90805 | C4 | semidirect |
| 18. C2×M16×C29 | C22 | semidirect |
| 23. C2×C4⋊Dic29 | C22 | semidirect |
| 24. #11745169 | C22 | semidirect |
| 25. #11745164 | C22 | semidirect |
| 42. #90805 | C2×C4 | semidirect |
| 45. C2×D116 | C2×C4 | semidirect |
| 51. C2×Dic58 | C2×C4 | semidirect |
| 85. D116 | C22×C4 | semidirect |
| 89. Dic58 | C22×C4 | semidirect |
| 111. C22×M16 | D29 | semidirect |
| 117. C2×C29 | #417 | semidirect |
| 133. C2×M16 | C2×D29 | semidirect |
| 141. C29 | C2×#417 | semidirect |
| 227. C2 | #14271165 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C22×C4⋊Dic29 | 2 |
| #14271165 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C22×M16×C29 | 2 |
| C2×#417 | 29 |