Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 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×#11745304 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. #14271172 | C2 | semidirect |
| 5. C2×#11745181 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C2×C29×#124 | C2 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 56. C42×C29 | D4 | semidirect |
| 66. #90777 | D4 | semidirect |
| 128. C2×#124 | D29 | semidirect |
| 160. C29 | #2004 | semidirect |
| 172. C2×Q8 | C22⋊D29 | semidirect |
| 200. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| #14271730 | 2 |
| C2×#11745153 | 2 |
| #14271172 | 2 |
| C2×#11745181 | 2 |
| #14270923 | 2 |
| C2×C29×#124 | 2 |
| #2004 | 29 |