Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11745236 | C2 | semidirect |
| 3. C2×C4×D116 | C2 | semidirect |
| 4. #14271359 | C2 | direct (N × H) |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C2×C29×C4⋊C8 | C2 | semidirect |
| 17. C2×D232 | C22 | semidirect |
| 19. #11745236 | C22 | semidirect |
| 21. C4×D116 | C22 | semidirect |
| 22. C29×C4⋊C8 | C22 | semidirect |
| 23. #11745169 | C22 | semidirect |
| 39. C2×D116 | D4 | semidirect |
| 62. C2×C4×C29 | D8 | semidirect |
| 78. D116 | C2×D4 | semidirect |
| 96. C4×C29 | C2×D8 | semidirect |
| 104. C2×C4⋊C8 | D29 | semidirect |
| 106. C2×C29 | #459 | semidirect |
| 127. C4⋊C8 | C2×D29 | semidirect |
| 129. C29 | C2×#459 | semidirect |
| 179. C2×C4 | D232 | semidirect |
| 202. C4 | C2×D232 | semidirect |
| 207. C2 | #14271359 | 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×#11745236 | 2 |
| C2×C4×D116 | 2 |
| #14271359 | 2 |
| C2×#11745169 | 2 |
| C2×C29×C4⋊C8 | 2 |
| C2×#459 | 29 |