Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#11745311 | C2 | semidirect |
| 2. C2×#11745302 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. C2×#11745181 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#535 | C2 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 44. C2×D4×C29 | D4 | semidirect |
| 55. C2×D116 | D4 | semidirect |
| 56. C4⋊C4×C29 | D4 | semidirect |
| 63. C4×Dic29 | D4 | semidirect |
| 67. #90777 | D4 | semidirect |
| 133. #535 | D29 | semidirect |
| 167. C29 | #2002 | semidirect |
| 174. C2×Q8 | C22⋊D29 | semidirect |
| 191. C2×D4 | C22⋊D29 | semidirect |
| 203. C4⋊C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×#11745302 | 2 |
| C2×#11745185 | 2 |
| #14271167 | 2 |
| C2×#11745181 | 2 |
| #14270922 | 2 |
| C29×#535 | 2 |
| #2002 | 29 |