Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14271571 | C2 | semidirect |
| 3. #14271569 | C2 | semidirect |
| 4. #14271567 | C2 | semidirect |
| 5. #14271565 | C2 | semidirect |
| 6. #14271564 | C2 | semidirect |
| 11. C29×#500 | C2 | semidirect |
| 66. #90772 | Q8 | semidirect |
| 67. C8×D29 | Q8 | semidirect |
| 108. #500 | D29 | semidirect |
| 146. C29 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271790 | 2 |
| #14271571 | 2 |
| #14271569 | 2 |
| #14271567 | 2 |
| #14271565 | 2 |
| #14271564 | 2 |
| #14271204 | 2 |
| #14271200 | 2 |
| #107×D29 | 2 |
| #14271117 | 2 |
| C29×#500 | 2 |
| #3164 | 29 |