Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11745153 | C2 | semidirect |
| 3. #14271165 | C2 | semidirect |
| 4. #14271164 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #14271065 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 12. #11745364 | C4 | semidirect |
| 20. C2×M16×C29 | C22 | semidirect |
| 21. C2×C42×C29 | C22 | semidirect |
| 23. C2×C4⋊Dic29 | C22 | semidirect |
| 24. C2×#90777 | C22 | semidirect |
| 95. Q8×C29 | C22⋊C4 | semidirect |
| 99. D4×C29 | C22⋊C4 | semidirect |
| 124. D116 | C22⋊C4 | semidirect |
| 129. Dic58 | C22⋊C4 | semidirect |
| 160. C2×#104 | D29 | semidirect |
| 186. C2×M16 | C2×D29 | semidirect |
| 189. C2×C42 | C2×D29 | semidirect |
| 197. C29 | #1792 | semidirect |
| 263. Q8 | #90781 | semidirect |
| 277. D4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| C2×#11745153 | 2 |
| #14271165 | 2 |
| #14271164 | 2 |
| C2×#11745171 | 2 |
| #14271065 | 2 |
| C2×C29×#104 | 2 |
| #1792 | 29 |