Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11745153 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. M16×Dic29 | C2 | semidirect |
| 6. C4×#90779 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 12. #11745309 | C4 | semidirect |
| 13. #11745306 | C4 | semidirect |
| 14. #11745302 | C4 | semidirect |
| 17. #11745298 | C4 | semidirect |
| 55. M16×C29 | D4 | semidirect |
| 73. #90777 | D4 | semidirect |
| 141. Dic29 | #104 | semidirect |
| 146. C2×#104 | D29 | semidirect |
| 179. C29 | #1980 | semidirect |
| 206. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271709 | 2 |
| C2×#11745153 | 2 |
| C2×#11745185 | 2 |
| C2×#11745173 | 2 |
| M16×Dic29 | 2 |
| C4×#90779 | 2 |
| C2×C29×#104 | 2 |
| #1980 | 29 |