Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C8×#1181 | C2 | semidirect |
| 4. C4⋊C4×#1181 | C2 | semidirect |
| 5. #14272037 | C2 | semidirect |
| 6. #14272036 | C2 | semidirect |
| 12. D4×#1181 | C4 | semidirect |
| 20. #11745223 | C4 | semidirect |
| 23. C29×#102 | C4 | semidirect |
| 24. #11745180 | C4 | semidirect |
| 25. #11745169 | C4 | semidirect |
| 26. #11745157 | C4 | semidirect |
| 49. C4⋊#1181 | C2×C4 | semidirect |
| 54. D29⋊C8 | C2×C4 | semidirect |
| 55. C2×C8×C29 | C2×C4 | semidirect |
| 56. C4⋊C4×C29 | C2×C4 | semidirect |
| 57. C4⋊Dic29 | C2×C4 | semidirect |
| 59. C2×#6597 | C2×C4 | semidirect |
| 85. D4×C29 | C42 | semidirect |
| 93. D116 | C42 | semidirect |
| 124. #1181 | #102 | direct (N × H) |
| 163. #102 | #1181 | direct (N × H) |
| 166. C29 | C4×#102 | semidirect |
| 190. C2×C8 | C2×#1181 | semidirect |
| 197. C4⋊C4 | C2×#1181 | semidirect |
| 216. D4 | C4×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1181 | 2 |
| C2×#11745223 | 2 |
| C2×C8×#1181 | 2 |
| C4⋊C4×#1181 | 2 |
| #14272037 | 2 |
| #14272036 | 2 |
| #102×D29 | 2 |
| C4×#102 | 29 |