Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 3. C2×#11745183 | C2 | direct (N × H) |
| 7. C22×Q8×C29 | C4 | semidirect |
| 16. #11745183 | C22 | direct (N × H) |
| 21. C2×Q8×C29 | C2×C4 | semidirect |
| 41. Q8×C29 | C22×C4 | semidirect |
| 53. C22×C29 | #103 | semidirect |
| 67. C2×C29 | C2×#103 | semidirect |
| 73. C22×Q8 | Dic29 | semidirect |
| 83. C29 | C22×#103 | semidirect |
| 88. C2×Q8 | C2×Dic29 | semidirect |
| 108. Q8 | C22×Dic29 | semidirect |
| 119. C22 | #11745183 | direct (N × H) |
| 129. C2 | C2×#11745183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6597 | 2 |
| C22×C4⋊Dic29 | 2 |
| C2×#11745183 | 2 |
| C23×Q8×C29 | 2 |
| C22×#103 | 29 |