Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #14272156 | C2 | semidirect |
| 4. (C2×#1181)⋊Q8 | C2 | semidirect |
| 5. #14272042 | C2 | semidirect |
| 6. #14272035 | C2 | semidirect |
| 19. C29×#137 | C4 | semidirect |
| 20. #11745313 | C4 | semidirect |
| 21. #11745304 | C4 | semidirect |
| 26. #11745271 | C4 | semidirect |
| 37. C2×Q8×C29 | C2×C4 | semidirect |
| 54. C2×Dic58 | C2×C4 | semidirect |
| 71. M16×C29 | C2×C4 | semidirect |
| 76. #90777 | C2×C4 | semidirect |
| 168. #137 | #1181 | semidirect |
| 186. C29 | #1882 | semidirect |
| 200. C2×Q8 | C2×#1181 | semidirect |
| 221. M16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272232 | 2 |
| D29⋊#104 | 2 |
| #14272156 | 2 |
| (C2×#1181)⋊Q8 | 2 |
| #14272042 | 2 |
| #14272035 | 2 |
| #137×D29 | 2 |
| #1882 | 29 |