Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 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×#90784 | C2 | semidirect |
| 3. #14271363 | C2 | direct (N × H) |
| 4. C2×C4⋊#6597 | C2 | semidirect |
| 5. C2×#11745157 | C2 | semidirect |
| 6. C2×C4×Q8×C29 | C2 | semidirect |
| 12. C4×Q8×C29 | C22 | semidirect |
| 18. C2×#90784 | C22 | semidirect |
| 22. #11745157 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 27. C2×Q8×C29 | D4 | semidirect |
| 58. Q8×C29 | C2×D4 | semidirect |
| 64. C2×C4×C29 | SD16 | semidirect |
| 90. C4×C29 | C2×SD16 | semidirect |
| 95. C2×C4×Q8 | D29 | semidirect |
| 99. C2×C29 | #460 | semidirect |
| 114. C4×Q8 | C2×D29 | semidirect |
| 121. C29 | C2×#460 | semidirect |
| 125. C2×Q8 | D116 | semidirect |
| 156. Q8 | C2×D116 | semidirect |
| 167. C2×C4 | #90784 | semidirect |
| 187. C4 | C2×#90784 | semidirect |
| 191. C2 | #14271363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745236 | 2 |
| #14271363 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745157 | 2 |
| C2×C4×Q8×C29 | 2 |
| C2×#460 | 29 |