Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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×#11745206 | C2 | semidirect |
| 2. C2×#11745209 | C2 | semidirect |
| 3. #14272080 | C2 | direct (N × H) |
| 7. C2×Q16×C29 | C4 | semidirect |
| 11. #11745281 | C4 | semidirect |
| 13. C2×D232 | C4 | semidirect |
| 17. #11745209 | C22 | semidirect |
| 19. #11745206 | C22 | semidirect |
| 33. Q16×C29 | C2×C4 | semidirect |
| 39. D232 | C2×C4 | semidirect |
| 85. C2×C29 | #360 | semidirect |
| 95. C2×Q16 | #1181 | semidirect |
| 105. C29 | C2×#360 | semidirect |
| 117. Q16 | C2×#1181 | semidirect |
| 169. C2 | #14272080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745206 | 2 |
| C2×#11745209 | 2 |
| #14272080 | 2 |
| C2×#11745281 | 2 |
| C2×#360 | 29 |