Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14271063 | C2 | semidirect |
| 3. #14271053 | C2 | semidirect |
| 4. #14271048 | C2 | semidirect |
| 5. #14271041 | C2 | semidirect |
| 6. #14271039 | C2 | semidirect |
| 7. #14271034 | C2 | semidirect |
| 8. #14271026 | C2 | semidirect |
| 9. C29×#380 | C2 | semidirect |
| 18. #11745292 | C4 | semidirect |
| 35. C22×C4×C29 | C2×C4 | semidirect |
| 42. C2×C22⋊D29 | C2×C4 | semidirect |
| 58. #90781 | C2×C4 | semidirect |
| 59. C4⋊Dic29 | C2×C4 | semidirect |
| 131. #380 | D29 | semidirect |
| 161. C29 | #2377 | semidirect |
| 176. C22×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| #14271063 | 2 |
| #14271053 | 2 |
| #14271048 | 2 |
| #14271041 | 2 |
| #14271039 | 2 |
| #14271034 | 2 |
| #14271026 | 2 |
| C29×#380 | 2 |
| #2377 | 29 |