Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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×#90782 | C2 | semidirect |
| 2. C2×#11745236 | C2 | semidirect |
| 3. #14271358 | C2 | direct (N × H) |
| 4. C2×C4⋊#6597 | C2 | semidirect |
| 5. C2×#11745157 | C2 | semidirect |
| 6. C2×C4×D4×C29 | C2 | semidirect |
| 13. C4×D4×C29 | C22 | semidirect |
| 18. C2×#90782 | C22 | semidirect |
| 21. #11745236 | C22 | semidirect |
| 22. #11745157 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 28. C2×D4×C29 | D4 | semidirect |
| 63. D4×C29 | C2×D4 | semidirect |
| 68. C2×C4×C29 | D8 | semidirect |
| 97. C4×C29 | C2×D8 | semidirect |
| 102. C2×C4×D4 | D29 | semidirect |
| 107. C2×C29 | #459 | semidirect |
| 123. C4×D4 | C2×D29 | semidirect |
| 129. C29 | C2×#459 | semidirect |
| 142. C2×D4 | D116 | semidirect |
| 174. D4 | C2×D116 | semidirect |
| 179. C2×C4 | #90782 | semidirect |
| 202. C4 | C2×#90782 | semidirect |
| 207. C2 | #14271358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×#11745236 | 2 |
| #14271358 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745157 | 2 |
| C2×C4×D4×C29 | 2 |
| C2×#459 | 29 |