Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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. M16×#1181 | C2 | semidirect |
| 4. C42×#1181 | C2 | semidirect |
| 5. #14272035 | C2 | semidirect |
| 6. #14272034 | C2 | semidirect |
| 9. Q8×#1181 | C4 | semidirect |
| 11. D4×#1181 | C4 | semidirect |
| 21. #11745226 | C4 | semidirect |
| 22. #11745224 | C4 | semidirect |
| 25. C29×#104 | C4 | semidirect |
| 26. #11745185 | C4 | semidirect |
| 27. #11745173 | C4 | semidirect |
| 28. #11745153 | C4 | semidirect |
| 54. C4×#1181 | C2×C4 | semidirect |
| 57. #90796 | C2×C4 | semidirect |
| 59. M16×C29 | C2×C4 | semidirect |
| 60. C42×C29 | C2×C4 | semidirect |
| 62. C4×Dic29 | C2×C4 | semidirect |
| 63. #90777 | C2×C4 | semidirect |
| 75. Q8×C29 | C42 | semidirect |
| 77. D4×C29 | C42 | semidirect |
| 88. D116 | C42 | semidirect |
| 98. Dic58 | C42 | semidirect |
| 113. #1181 | #104 | direct (N × H) |
| 153. #104 | #1181 | direct (N × H) |
| 156. C29 | C4×#104 | semidirect |
| 176. M16 | C2×#1181 | semidirect |
| 193. C42 | C2×#1181 | semidirect |
| 198. Q8 | C4×#1181 | semidirect |
| 205. D4 | C4×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#1181 | 2 |
| D29⋊#104 | 2 |
| M16×#1181 | 2 |
| C42×#1181 | 2 |
| #14272035 | 2 |
| #14272034 | 2 |
| #104×D29 | 2 |
| C4×#104 | 29 |