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 |
|---|---|---|
| 2. C2×#11745231 | C2 | semidirect |
| 4. #14271369 | C2 | direct (N × H) |
| 5. C2×#11745164 | C2 | semidirect |
| 6. C2×C29×C4⋊C8 | C2 | semidirect |
| 21. #11745231 | C22 | semidirect |
| 22. C29×C4⋊C8 | C22 | semidirect |
| 23. #11745164 | C22 | semidirect |
| 56. C2×C4×C29 | SD16 | semidirect |
| 86. C4×C29 | C2×SD16 | semidirect |
| 95. C2×C4⋊C8 | D29 | semidirect |
| 97. C2×C29 | #461 | semidirect |
| 117. C4⋊C8 | C2×D29 | semidirect |
| 119. C29 | C2×#461 | semidirect |
| 163. C2×C4 | #90773 | semidirect |
| 183. C4 | C2×#90773 | semidirect |
| 187. C2 | #14271369 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745231 | 2 |
| C2×C4×D116 | 2 |
| #14271369 | 2 |
| C2×#11745164 | 2 |
| C2×C29×C4⋊C8 | 2 |
| C2×#461 | 29 |