Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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. C22×#90779 | C2 | semidirect |
| 4. #14271022 | C2 | direct (N × H) |
| 5. C2×#11745179 | C2 | semidirect |
| 6. C2×C29×#95 | C2 | semidirect |
| 13. C22×C4×D29 | C4 | semidirect |
| 18. C2×#90779 | C22 | semidirect |
| 19. C29×#95 | C22 | semidirect |
| 20. #11745179 | C22 | semidirect |
| 44. C2×C4×D29 | C2×C4 | semidirect |
| 59. C22×D29 | C4⋊C4 | semidirect |
| 74. C2×Dic29 | C22⋊C4 | semidirect |
| 94. C2×D29 | C2×C4⋊C4 | semidirect |
| 98. Dic29 | C2×C22⋊C4 | semidirect |
| 104. C2×#95 | D29 | semidirect |
| 105. C2×C29 | #380 | semidirect |
| 125. #95 | C2×D29 | semidirect |
| 126. C29 | C2×#380 | semidirect |
| 205. C2 | #14271022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D29 | 2 |
| C22×#90779 | 2 |
| C22×#90781 | 2 |
| #14271022 | 2 |
| C2×#11745179 | 2 |
| C2×C29×#95 | 2 |
| C2×#380 | 29 |