Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745231 | C2 | semidirect |
| 3. #14271523 | C2 | direct (N × H) |
| 4. C2×#11745164 | C2 | semidirect |
| 6. C2×C29×#97 | C2 | semidirect |
| 19. #11745231 | C22 | semidirect |
| 20. C29×#97 | C22 | semidirect |
| 22. #11745164 | C22 | semidirect |
| 88. C2×#97 | D29 | semidirect |
| 89. C2×C29 | #489 | semidirect |
| 109. #97 | C2×D29 | semidirect |
| 110. C29 | C2×#489 | semidirect |
| 171. C2 | #14271523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745231 | 2 |
| C2×#11745237 | 2 |
| #14271523 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C2×C29×#97 | 2 |
| C2×#489 | 29 |