Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
544 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 544 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 |
|---|---|---|
| 2. C2×#11745231 | C2 | semidirect |
| 3. #14271368 | C2 | direct (N × H) |
| 4. C2×C4⋊#6597 | C2 | semidirect |
| 5. C2×#11745158 | C2 | semidirect |
| 21. #11745231 | C22 | semidirect |
| 22. #11745158 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 62. C2×C4×C29 | SD16 | semidirect |
| 87. C4×C29 | C2×SD16 | semidirect |
| 98. C2×C29 | #461 | semidirect |
| 119. C29 | C2×#461 | semidirect |
| 163. C2×C4 | #90783 | semidirect |
| 183. C4 | C2×#90783 | semidirect |
| 187. C2 | #14271368 | 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 |
| C2×#11745231 | 2 |
| #14271368 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745158 | 2 |
| C2×C4×D4×C29 | 2 |
| C2×#461 | 29 |