Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 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. #14271074 | C2 | direct (N × H) |
| 3. C2×#11745179 | C2 | semidirect |
| 4. C23×Q8×C29 | C2 | semidirect |
| 7. C22×Q8×C29 | C22 | semidirect |
| 12. #11745179 | C22 | semidirect |
| 16. C23×D29 | Q8 | semidirect |
| 36. C22×D29 | C2×Q8 | semidirect |
| 57. C23×Q8 | D29 | semidirect |
| 61. C2×C29 | #393 | semidirect |
| 68. C22×Q8 | C2×D29 | semidirect |
| 74. C29 | C2×#393 | semidirect |
| 119. C2 | #14271074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90781 | 2 |
| #14271074 | 2 |
| C2×#11745179 | 2 |
| C23×Q8×C29 | 2 |
| C2×#393 | 29 |