Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. #14271223 | C2 | semidirect |
| 3. #14271215 | C2 | semidirect |
| 4. #14271190 | C2 | semidirect |
| 7. M16×Dic29 | C2 | semidirect |
| 8. C2×C8×Dic29 | C2 | semidirect |
| 9. C29×#424 | C2 | semidirect |
| 94. #424 | D29 | semidirect |
| 123. C29 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271631 | 2 |
| #14271223 | 2 |
| #14271215 | 2 |
| #14271190 | 2 |
| #14271131 | 2 |
| #14271129 | 2 |
| M16×Dic29 | 2 |
| C2×C8×Dic29 | 2 |
| C29×#424 | 2 |
| #2922 | 29 |