Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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. #14272231 | C2 | semidirect |
| 2. #14272144 | C2 | semidirect |
| 3. #14272142 | C2 | semidirect |
| 5. C22×Q8×C29 | C4 | semidirect |
| 7. C2×#90809 | C4 | semidirect |
| 9. C2×Q8×D29 | C4 | semidirect |
| 11. C2×#90805 | C4 | semidirect |
| 88. C22×Q8 | #1181 | semidirect |
| 93. C29 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272231 | 2 |
| #14272144 | 2 |
| #14272142 | 2 |
| C2×#11745362 | 2 |
| #2884 | 29 |