Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14272099 | C2 | semidirect |
| 5. #14272035 | C2 | semidirect |
| 6. #14272034 | C2 | semidirect |
| 9. Q8×#1181 | C4 | semidirect |
| 11. D4×#1181 | C4 | semidirect |
| 20. #11745226 | C4 | semidirect |
| 21. #11745224 | C4 | semidirect |
| 25. C29×#104 | C4 | semidirect |
| 26. #11745185 | C4 | semidirect |
| 27. #11745173 | C4 | semidirect |
| 28. #11745153 | C4 | semidirect |
| 53. C4×#1181 | C2×C4 | semidirect |
| 56. #90796 | C2×C4 | semidirect |
| 58. M16×C29 | C2×C4 | semidirect |
| 59. C42×C29 | C2×C4 | semidirect |
| 61. C4×Dic29 | C2×C4 | semidirect |
| 62. #90777 | C2×C4 | semidirect |
| 151. #104 | #1181 | semidirect |
| 155. C29 | #1759 | semidirect |
| 175. M16 | C2×#1181 | semidirect |
| 191. C42 | 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 |
| D29⋊#104 | 2 |
| M16×#1181 | 2 |
| #14272099 | 2 |
| #14272035 | 2 |
| #14272034 | 2 |
| #104×D29 | 2 |
| #1759 | 29 |