Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×#1181 | C2 | semidirect |
| 2. #14272115 | C2 | semidirect |
| 3. #14272109 | C2 | semidirect |
| 4. C42×#1181 | C2 | semidirect |
| 13. C29×#127 | C4 | semidirect |
| 14. #11745302 | C4 | semidirect |
| 15. #11745236 | C4 | semidirect |
| 22. C2×D4×C29 | C2×C4 | semidirect |
| 23. C2×C22⋊D29 | C2×C4 | semidirect |
| 26. C2×D116 | C2×C4 | semidirect |
| 31. C4×#1181 | D4 | semidirect |
| 32. C42×C29 | C2×C4 | semidirect |
| 33. C4×Dic29 | C2×C4 | semidirect |
| 61. #1181 | #127 | direct (N × H) |
| 62. C4×C29 | C4×D4 | semidirect |
| 63. Dic29 | C4×D4 | semidirect |
| 78. #127 | #1181 | direct (N × H) |
| 85. C29 | C4×#127 | semidirect |
| 91. C2×D4 | C2×#1181 | semidirect |
| 102. C42 | C2×#1181 | semidirect |
| 131. C4 | D4×#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 |
| #14272115 | 2 |
| #14272109 | 2 |
| C42×#1181 | 2 |
| #127×D29 | 2 |
| C4×#127 | 29 |