Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #14271719 | C2 | direct (N × H) |
| 2. C2×#11745250 | C2 | semidirect |
| 3. C2×#11745232 | C2 | semidirect |
| 5. C2×#11745249 | C2 | semidirect |
| 8. C2×C29×#125 | C2 | semidirect |
| 12. C29×#125 | C22 | semidirect |
| 25. #11745250 | C22 | semidirect |
| 26. #11745249 | C22 | semidirect |
| 28. #11745232 | C22 | semidirect |
| 37. C2×C4×D29 | Q8 | semidirect |
| 69. C4×D29 | C2×Q8 | semidirect |
| 87. C2×#125 | D29 | semidirect |
| 92. C2×C29 | #533 | semidirect |
| 101. #125 | C2×D29 | semidirect |
| 116. C29 | C2×#533 | semidirect |
| 172. C2 | #14271719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271719 | 2 |
| C2×#11745250 | 2 |
| C2×#11745232 | 2 |
| C2×#11745258 | 2 |
| C2×#11745249 | 2 |
| C2×#11745254 | 2 |
| C2×C42×D29 | 2 |
| C2×C29×#125 | 2 |
| C2×#533 | 29 |