Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 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×D232 | C2 | semidirect |
| 2. C2×#11745292 | C2 | semidirect |
| 3. #14271416 | C2 | direct (N × H) |
| 4. C2×#11745165 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C22×M16×C29 | C2 | semidirect |
| 11. C2×M16×C29 | C22 | semidirect |
| 15. #11745292 | C22 | semidirect |
| 19. C2×D232 | C22 | semidirect |
| 20. #11745169 | C22 | semidirect |
| 21. #11745165 | C22 | semidirect |
| 39. C2×C8×C29 | D4 | semidirect |
| 70. C8×C29 | C2×D4 | semidirect |
| 88. C22×M16 | D29 | semidirect |
| 94. C2×C29 | #469 | semidirect |
| 104. C2×M16 | C2×D29 | semidirect |
| 113. C29 | C2×#469 | semidirect |
| 132. C2×C8 | C22⋊D29 | semidirect |
| 162. C8 | C2×C22⋊D29 | semidirect |
| 180. C2 | #14271416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745292 | 2 |
| #14271416 | 2 |
| C2×#11745165 | 2 |
| C2×#11745169 | 2 |
| C22×M16×C29 | 2 |
| C2×#469 | 29 |