Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745271 | C2 | semidirect |
| 2. C2×#11745304 | C2 | semidirect |
| 3. C2×#11745313 | C2 | semidirect |
| 5. C2×#11745306 | C2 | semidirect |
| 6. #14271556 | C2 | semidirect |
| 7. #14271554 | C2 | semidirect |
| 8. #14271541 | C2 | semidirect |
| 9. #14271534 | C2 | semidirect |
| 10. M16×Dic29 | C2 | semidirect |
| 11. C2×C29×#137 | C2 | semidirect |
| 70. M16×C29 | D4 | semidirect |
| 84. #90777 | D4 | semidirect |
| 141. Dic29 | #137 | semidirect |
| 145. C2×#137 | D29 | semidirect |
| 189. C29 | #3152 | semidirect |
| 224. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745304 | 2 |
| C2×#11745313 | 2 |
| #14271709 | 2 |
| C2×#11745306 | 2 |
| #14271556 | 2 |
| #14271554 | 2 |
| #14271541 | 2 |
| #14271534 | 2 |
| M16×Dic29 | 2 |
| C2×C29×#137 | 2 |
| #3152 | 29 |