Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 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 |
|---|---|---|
| 3. #14271365 | C2 | direct (N × H) |
| 4. C2×C4⋊#6597 | C2 | semidirect |
| 5. C2×#11745183 | C2 | semidirect |
| 6. C2×C29×C4⋊Q8 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 22. #11745183 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 61. C2×C4×C29 | SD16 | semidirect |
| 87. C4×C29 | C2×SD16 | semidirect |
| 92. C2×C4⋊Q8 | D29 | semidirect |
| 97. C2×C29 | #461 | semidirect |
| 109. C4⋊Q8 | C2×D29 | semidirect |
| 119. C29 | C2×#461 | semidirect |
| 163. C2×C4 | #90784 | semidirect |
| 183. C4 | C2×#90784 | semidirect |
| 187. C2 | #14271365 | 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×C4×D116 | 2 |
| #14271365 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745183 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| C2×#461 | 29 |