Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C42×D29 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. #14271126 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 13. #11745308 | C4 | semidirect |
| 14. #11745300 | C4 | semidirect |
| 32. C2×Q8×C29 | C2×C4 | semidirect |
| 34. C2×D4×C29 | C2×C4 | semidirect |
| 53. C42×C29 | D4 | semidirect |
| 57. C4⋊Dic29 | C2×C4 | semidirect |
| 62. C4×Dic29 | D4 | semidirect |
| 114. C2×D29 | #104 | semidirect |
| 127. C2×#104 | D29 | semidirect |
| 156. C29 | #1896 | semidirect |
| 162. C2×Q8 | C4×D29 | semidirect |
| 165. C2×D4 | C4×D29 | semidirect |
| 195. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271670 | 2 |
| C2×C42×D29 | 2 |
| C2×#11745185 | 2 |
| #14271126 | 2 |
| #14270924 | 2 |
| #14270923 | 2 |
| C2×C29×#104 | 2 |
| #1896 | 29 |