Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 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 |
|---|---|---|
| 2. C22×#90785 | C2 | semidirect |
| 4. #14271317 | C2 | direct (N × H) |
| 5. C2×#11745164 | C2 | semidirect |
| 6. C2×#11745183 | C2 | semidirect |
| 8. C22×Q16×C29 | C2 | semidirect |
| 20. C2×Q16×C29 | C22 | semidirect |
| 25. C2×#90785 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 32. #11745164 | C22 | semidirect |
| 76. C22×D29 | Q16 | semidirect |
| 116. C2×D29 | C2×Q16 | semidirect |
| 127. C22×Q16 | D29 | semidirect |
| 133. C2×C29 | #451 | semidirect |
| 151. C2×Q16 | C2×D29 | semidirect |
| 162. C29 | C2×#451 | semidirect |
| 255. C2 | #14271317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D29 | 2 |
| C22×#90785 | 2 |
| C2×#11745308 | 2 |
| #14271317 | 2 |
| C2×#11745164 | 2 |
| C2×#11745183 | 2 |
| C2×#11745168 | 2 |
| C22×Q16×C29 | 2 |
| C2×#451 | 29 |