Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1624 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 725 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×#11745306 | C2 | direct (N × H) |
| 14. #11745306 | C22 | direct (N × H) |
| 25. C22×Dic29 | Q8 | semidirect |
| 41. C2×Dic29 | C2×Q8 | semidirect |
| 46. C22×C29 | C4⋊Q8 | semidirect |
| 53. Dic29 | C22×Q8 | semidirect |
| 59. C2×C29 | C2×C4⋊Q8 | semidirect |
| 73. C29 | C22×C4⋊Q8 | semidirect |
| 102. C22 | #11745306 | direct (N × H) |
| 110. C2 | C2×#11745306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C2×#11745306 | 2 |
| C22×#90779 | 2 |
| C22×C4×Dic29 | 2 |
| C23×Q8×C29 | 2 |
| C22×C4⋊Q8 | 29 |