Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 293 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. #14271205 | C2 | semidirect |
| 3. #14271201 | C2 | semidirect |
| 6. C2×M16×C29 | C4 | semidirect |
| 16. #11745166 | C22 | semidirect |
| 17. #11745165 | C22 | semidirect |
| 26. M16×C29 | C2×C4 | semidirect |
| 27. C2×C8×C29 | C2×C4 | semidirect |
| 72. C2×M16 | Dic29 | semidirect |
| 84. C29 | #2911 | semidirect |
| 93. M16 | C2×Dic29 | semidirect |
| 94. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745288 | 2 |
| #14271205 | 2 |
| #14271201 | 2 |
| C22×M16×C29 | 2 |
| #2911 | 29 |