Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271496 | C2 | semidirect |
| 3. #14271440 | C2 | semidirect |
| 4. #14271365 | C2 | semidirect |
| 6. #14271261 | C2 | semidirect |
| 7. #14271220 | C2 | semidirect |
| 8. C29×#533 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 12. C29×C4⋊Q8 | C22 | semidirect |
| 17. C4×Q8×C29 | C22 | semidirect |
| 27. #11745183 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. #11745151 | C22 | semidirect |
| 108. #533 | D29 | semidirect |
| 124. C4⋊Q8 | C2×D29 | semidirect |
| 125. C4⋊Q8 | C2×D29 | semidirect |
| 130. C4×Q8 | C2×D29 | semidirect |
| 145. C29 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271496 | 2 |
| #14271440 | 2 |
| #14271365 | 2 |
| #14271313 | 2 |
| #14271261 | 2 |
| #14271220 | 2 |
| C29×#533 | 2 |
| #3110 | 29 |