Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. #14272174 | C2 | semidirect |
| 4. #14272107 | C2 | semidirect |
| 5. #14272042 | C2 | semidirect |
| 6. #14272034 | C2 | semidirect |
| 25. C29×#104 | C4 | semidirect |
| 26. #11745185 | C4 | semidirect |
| 27. #11745173 | C4 | semidirect |
| 28. #11745153 | 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 |
| 155. #104 | #1181 | semidirect |
| 159. C29 | #1860 | semidirect |
| 179. M16 | C2×#1181 | semidirect |
| 195. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272232 | 2 |
| #14272174 | 2 |
| #14272154 | 2 |
| #14272107 | 2 |
| #14272042 | 2 |
| #14272034 | 2 |
| #104×D29 | 2 |
| #1860 | 29 |