Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #14271898 | C2 | semidirect |
| 2. #14271873 | C2 | semidirect |
| 3. #14271518 | C2 | semidirect |
| 4. #14271510 | C2 | semidirect |
| 5. #14271464 | C2 | semidirect |
| 6. #14271459 | C2 | semidirect |
| 7. #14271379 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. C4×D232 | C2 | semidirect |
| 11. C8×Q8×C29 | C2 | semidirect |
| 126. C8×Q8 | D29 | semidirect |
| 163. C29 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271898 | 2 |
| #14271873 | 2 |
| #14271518 | 2 |
| #14271510 | 2 |
| #14271464 | 2 |
| #14271459 | 2 |
| #14271379 | 2 |
| #14271359 | 2 |
| C4×#90773 | 2 |
| C4×D232 | 2 |
| C8×Q8×C29 | 2 |
| #3361 | 29 |