Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C22×#90772 | C2 | semidirect |
| 3. #14271242 | C2 | direct (N × H) |
| 4. C2×C4⋊#6597 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. C2×C4×C8×C29 | C2 | semidirect |
| 16. C2×#90772 | C22 | semidirect |
| 19. C4×C8×C29 | C22 | semidirect |
| 20. #11745168 | C22 | semidirect |
| 21. C4⋊#6597 | C22 | semidirect |
| 34. C2×C8×C29 | D4 | semidirect |
| 50. C2×C4×C29 | M16 | semidirect |
| 64. C8×C29 | C2×D4 | semidirect |
| 77. C4×C29 | C2×M16 | semidirect |
| 86. C2×C4×C8 | D29 | semidirect |
| 87. C2×C29 | #436 | semidirect |
| 106. C4×C8 | C2×D29 | semidirect |
| 107. C29 | C2×#436 | semidirect |
| 123. C2×C8 | D116 | semidirect |
| 142. C2×C4 | #90772 | semidirect |
| 151. C8 | C2×D116 | semidirect |
| 163. C4 | C2×#90772 | semidirect |
| 167. C2 | #14271242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×C4×D116 | 2 |
| #14271242 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745168 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×#436 | 29 |