Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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×#90783 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. C2×#11745237 | C2 | semidirect |
| 4. #14271550 | C2 | direct (N × H) |
| 5. C2×#11745151 | C2 | semidirect |
| 6. C2×C29×#127 | C2 | semidirect |
| 12. C29×#127 | C22 | semidirect |
| 15. C2×#90783 | C22 | semidirect |
| 17. C2×#90782 | C22 | semidirect |
| 21. #11745237 | C22 | semidirect |
| 22. #11745151 | C22 | semidirect |
| 45. C2×#6597 | D4 | semidirect |
| 69. #6597 | C2×D4 | semidirect |
| 86. C2×#127 | D29 | semidirect |
| 91. C2×C29 | #496 | semidirect |
| 105. #127 | C2×D29 | semidirect |
| 111. C29 | C2×#496 | semidirect |
| 174. C2 | #14271550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C22×#90782 | 2 |
| C2×#11745237 | 2 |
| #14271550 | 2 |
| C2×#11745151 | 2 |
| C2×C29×#127 | 2 |
| C2×#496 | 29 |