Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #14272207 | C2 | semidirect |
| 2. #14272205 | C2 | semidirect |
| 3. #14272092 | C2 | semidirect |
| 4. #14272078 | C2 | semidirect |
| 5. #14272077 | C2 | semidirect |
| 6. C16×#1181 | C2 | semidirect |
| 18. C29×SD32 | C4 | semidirect |
| 19. #11745177 | C4 | semidirect |
| 20. #11745174 | C4 | semidirect |
| 21. #11745148 | C4 | semidirect |
| 85. SD32 | #1181 | semidirect |
| 94. C29 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272207 | 2 |
| #14272205 | 2 |
| #14272092 | 2 |
| #14272078 | 2 |
| #14272077 | 2 |
| C16×#1181 | 2 |
| #14271594 | 2 |
| #2178 | 29 |