Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 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. #41×#1181 | C2 | semidirect |
| 2. #14272160 | C2 | semidirect |
| 3. C2×#11745224 | C2 | semidirect |
| 4. #14272143 | C2 | semidirect |
| 5. #14272046 | C2 | semidirect |
| 6. #14272035 | C2 | semidirect |
| 19. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 20. #11745313 | C4 | semidirect |
| 21. #11745294 | C4 | semidirect |
| 26. #11745271 | C4 | semidirect |
| 36. C2×D4×C29 | C2×C4 | semidirect |
| 53. C2×Dic58 | C2×C4 | semidirect |
| 71. M16×C29 | C2×C4 | semidirect |
| 76. #90777 | C2×C4 | semidirect |
| 165. AGL(1,ℤ/8) | #1181 | semidirect |
| 183. C29 | #1906 | semidirect |
| 199. C2×D4 | C2×#1181 | semidirect |
| 217. M16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#1181 | 2 |
| #14272160 | 2 |
| C2×#11745224 | 2 |
| #14272143 | 2 |
| #14272046 | 2 |
| #14272035 | 2 |
| #14271959 | 2 |
| #1906 | 29 |