Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic116 | C2 | semidirect |
| 4. #14271405 | C2 | direct (N × H) |
| 5. C2×#11745158 | C2 | semidirect |
| 6. C2×C29×#107 | C2 | semidirect |
| 15. C2×Dic116 | C22 | semidirect |
| 20. C29×#107 | C22 | semidirect |
| 21. #11745158 | C22 | semidirect |
| 48. C22×D29 | Q16 | semidirect |
| 76. C2×D29 | C2×Q16 | semidirect |
| 87. C2×#107 | D29 | semidirect |
| 89. C2×C29 | #467 | semidirect |
| 107. #107 | C2×D29 | semidirect |
| 109. C29 | C2×#467 | semidirect |
| 171. C2 | #14271405 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic116 | 2 |
| C22×C8×D29 | 2 |
| C2×#11745259 | 2 |
| #14271405 | 2 |
| C2×#11745158 | 2 |
| C2×C29×#107 | 2 |
| C2×#467 | 29 |