Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#11745148 | C2 | semidirect |
| 2. #14271404 | C2 | semidirect |
| 4. #14270991 | C2 | semidirect |
| 5. #14270968 | C2 | semidirect |
| 6. #14270965 | C2 | semidirect |
| 7. C22×C16×C29 | C2 | semidirect |
| 39. C16×C29 | D4 | semidirect |
| 60. C22×C29 | SD32 | semidirect |
| 72. C22×C16 | D29 | semidirect |
| 96. C29 | #2217 | semidirect |
| 115. C16 | C22⋊D29 | semidirect |
| 138. C22 | #11745148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745148 | 2 |
| #14271404 | 2 |
| #14271399 | 2 |
| #14270991 | 2 |
| #14270968 | 2 |
| #14270965 | 2 |
| C22×C16×C29 | 2 |
| #2217 | 29 |