Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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 |
|---|---|---|
| 1. #14271774 | C2 | direct (N × H) |
| 3. C2×#11745232 | C2 | semidirect |
| 4. C2×#11745251 | C2 | semidirect |
| 6. C2×Q8×Dic29 | C2 | semidirect |
| 8. C2×C29×C4⋊Q8 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 15. Q8×Dic29 | C22 | semidirect |
| 26. #11745251 | C22 | semidirect |
| 28. #11745232 | C22 | semidirect |
| 83. C2×C4⋊Q8 | D29 | semidirect |
| 90. C2×C29 | #541 | semidirect |
| 96. C4⋊Q8 | C2×D29 | semidirect |
| 114. C29 | C2×#541 | semidirect |
| 168. C2 | #14271774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271774 | 2 |
| C2×#11745260 | 2 |
| C2×#11745232 | 2 |
| C2×#11745251 | 2 |
| C2×#11745308 | 2 |
| C2×Q8×Dic29 | 2 |
| C2×#11745234 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| C2×#541 | 29 |