Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #14271570 | C2 | semidirect |
| 4. #14271568 | C2 | semidirect |
| 5. #14271566 | C2 | semidirect |
| 6. #14271559 | C2 | semidirect |
| 9. C29×#498 | C2 | semidirect |
| 65. #90772 | Q8 | semidirect |
| 86. C8×C29 | C2×Q8 | semidirect |
| 87. #6597 | C2×Q8 | semidirect |
| 109. #498 | D29 | semidirect |
| 141. C29 | #3165 | semidirect |
| 194. C8 | Q8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4⋊Q8×D29 | 2 |
| #14271570 | 2 |
| #14271568 | 2 |
| #14271566 | 2 |
| #14271559 | 2 |
| #14271202 | 2 |
| C4×#90772 | 2 |
| C29×#498 | 2 |
| #3165 | 29 |