Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271565 | C2 | semidirect |
| 4. #14271562 | C2 | semidirect |
| 5. #14271560 | C2 | semidirect |
| 9. C29×#499 | C2 | semidirect |
| 46. C8×D29 | Q8 | semidirect |
| 47. C8×D29 | Q8 | semidirect |
| 78. #499 | D29 | semidirect |
| 105. C29 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271719 | 2 |
| #14271567 | 2 |
| #14271565 | 2 |
| #14271562 | 2 |
| #14271560 | 2 |
| #14271200 | 2 |
| #14271198 | 2 |
| C4×C8×D29 | 2 |
| C29×#499 | 2 |
| #3160 | 29 |