Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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. #14271220 | C2 | semidirect |
| 2. #14271009 | C2 | semidirect |
| 3. #14270897 | C2 | semidirect |
| 6. C29×C4⋊Q8 | C4 | semidirect |
| 7. C29×#127 | C4 | semidirect |
| 12. C4×D4×C29 | C4 | semidirect |
| 89. C4⋊Q8 | Dic29 | semidirect |
| 90. #127 | Dic29 | semidirect |
| 95. C4×D4 | Dic29 | semidirect |
| 103. C29 | #1505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271220 | 2 |
| #14271009 | 2 |
| #14270897 | 2 |
| C29×#532 | 2 |
| #1505 | 29 |