Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #14271567 | C2 | semidirect |
| 3. #14271564 | C2 | semidirect |
| 4. #14271563 | C2 | semidirect |
| 5. #14271560 | C2 | semidirect |
| 32. C2×C8×C29 | Q8 | semidirect |
| 47. C2×#6597 | Q8 | semidirect |
| 107. C29 | #3160 | semidirect |
| 114. C2×C8 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| #14271567 | 2 |
| #14271564 | 2 |
| #14271563 | 2 |
| #14271560 | 2 |
| #14271201 | 2 |
| #14271199 | 2 |
| C2×C8×Dic29 | 2 |
| C29×#427 | 2 |
| #3160 | 29 |