Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×D232 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. C2×#11745302 | C2 | semidirect |
| 4. #14271538 | C2 | direct (N × H) |
| 5. C2×C8×Dic29 | C2 | semidirect |
| 6. C22×D8×C29 | C2 | semidirect |
| 11. C2×D8×C29 | C22 | semidirect |
| 14. #11745302 | C22 | semidirect |
| 16. C2×#90782 | C22 | semidirect |
| 20. C2×D232 | C22 | semidirect |
| 21. C8×Dic29 | C22 | semidirect |
| 37. C2×C8×C29 | D4 | semidirect |
| 42. C2×#6597 | D4 | semidirect |
| 60. C2×Dic29 | D8 | semidirect |
| 65. C8×C29 | C2×D4 | semidirect |
| 66. #6597 | C2×D4 | semidirect |
| 80. Dic29 | C2×D8 | semidirect |
| 83. C22×D8 | D29 | semidirect |
| 88. C2×C29 | #493 | semidirect |
| 100. C2×D8 | C2×D29 | semidirect |
| 107. C29 | C2×#493 | semidirect |
| 127. C2×C8 | C22⋊D29 | semidirect |
| 152. C8 | C2×C22⋊D29 | semidirect |
| 168. C2 | #14271538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C22×#90782 | 2 |
| C2×#11745302 | 2 |
| #14271538 | 2 |
| C2×C8×Dic29 | 2 |
| C22×D8×C29 | 2 |
| C2×#493 | 29 |