Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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. #14272142 | C2 | semidirect |
| 2. #14272069 | C2 | semidirect |
| 3. #14272067 | C2 | semidirect |
| 5. C2×#41×C29 | C4 | semidirect |
| 9. #11745306 | C4 | semidirect |
| 12. #11745298 | C4 | semidirect |
| 14. C2×C4×Dic29 | C4 | semidirect |
| 91. C2×#41 | #1181 | semidirect |
| 102. C29 | #2126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272142 | 2 |
| #14272069 | 2 |
| #14272067 | 2 |
| #14271709 | 2 |
| #2126 | 29 |