Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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. #14272174 | C2 | semidirect |
| 3. #14272173 | C2 | semidirect |
| 13. C2×M16×C29 | C4 | semidirect |
| 14. C2×#90777 | C4 | semidirect |
| 15. M16×D29 | C4 | semidirect |
| 17. C2×#90772 | C4 | semidirect |
| 19. #11745210 | C22 | semidirect |
| 20. #11745209 | C22 | semidirect |
| 39. M16×C29 | C2×C4 | semidirect |
| 40. C2×C8×C29 | C2×C4 | semidirect |
| 41. #90777 | C2×C4 | semidirect |
| 42. C2×#6597 | C2×C4 | semidirect |
| 43. #90772 | C2×C4 | semidirect |
| 44. C8×D29 | C2×C4 | semidirect |
| 107. C2×M16 | #1181 | semidirect |
| 118. C29 | #2911 | semidirect |
| 133. M16 | C2×#1181 | semidirect |
| 137. C2×C8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| #14272174 | 2 |
| #14272173 | 2 |
| C2×M16×D29 | 2 |
| #2911 | 29 |