Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
540 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 229 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. #14271062 | C2 | semidirect |
| 3. #14271056 | C2 | semidirect |
| 4. #14271026 | C2 | semidirect |
| 5. #14271023 | C2 | semidirect |
| 6. C4×C4⋊Dic29 | C2 | semidirect |
| 7. #14271009 | C2 | semidirect |
| 11. C4×D4×C29 | C4 | semidirect |
| 107. C4×D4 | Dic29 | semidirect |
| 122. C29 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271066 | 2 |
| #14271062 | 2 |
| #14271056 | 2 |
| #14271026 | 2 |
| #14271023 | 2 |
| C4×C4⋊Dic29 | 2 |
| #14271009 | 2 |
| C2×C4×D4×C29 | 2 |
| #2319 | 29 |