Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 15. C29×#106 | C4 | semidirect |
| 16. #11745165 | C4 | semidirect |
| 17. #11745156 | C4 | semidirect |
| 57. C8×C29 | C4⋊C4 | semidirect |
| 58. #6597 | C4⋊C4 | semidirect |
| 93. #106 | #1181 | semidirect |
| 96. C29 | #1944 | semidirect |
| 137. C8 | C4⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745210 | 2 |
| C2×#11745208 | 2 |
| #14272114 | 2 |
| #14272036 | 2 |
| #106×D29 | 2 |
| #1944 | 29 |