Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14271727 | C2 | semidirect |
| 3. C2×#11745236 | C2 | semidirect |
| 4. #14271169 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 37. C2×D4×C29 | D4 | semidirect |
| 55. C2×D116 | D4 | semidirect |
| 60. C42×C29 | D4 | semidirect |
| 65. C4⋊Dic29 | D4 | semidirect |
| 68. #90777 | D4 | semidirect |
| 135. C2×#104 | D29 | semidirect |
| 167. C29 | #2002 | semidirect |
| 174. C2×Q8 | D116 | semidirect |
| 191. C2×D4 | D116 | semidirect |
| 208. C42 | 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 |
| #14271727 | 2 |
| C2×#11745236 | 2 |
| #14271169 | 2 |
| C2×#11745171 | 2 |
| #14270923 | 2 |
| C2×C29×#104 | 2 |
| #2002 | 29 |