Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 1. D29⋊#108 | C2 | semidirect |
| 2. #14272156 | C2 | semidirect |
| 4. D29⋊#101 | C2 | semidirect |
| 6. #14272126 | C2 | semidirect |
| 14. C2×SD16×C29 | C4 | semidirect |
| 15. C2×#90784 | C4 | semidirect |
| 16. C2×#90783 | C4 | semidirect |
| 21. C2×#90773 | C4 | semidirect |
| 150. C2×SD16 | #1181 | semidirect |
| 164. C29 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#108 | 2 |
| #14272156 | 2 |
| #14272155 | 2 |
| D29⋊#101 | 2 |
| D29⋊#100 | 2 |
| #14272126 | 2 |
| C2×SD16×D29 | 2 |
| #1977 | 29 |