Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14271720 | C2 | semidirect |
| 3. #14271561 | C2 | semidirect |
| 4. #14271536 | C2 | semidirect |
| 5. #14271514 | C2 | semidirect |
| 6. #14271510 | C2 | semidirect |
| 7. #14271392 | C2 | semidirect |
| 8. C4×#90773 | C2 | semidirect |
| 9. C2×C4×C8×C29 | C2 | semidirect |
| 71. C2×C4×C29 | SD16 | semidirect |
| 90. C8×C29 | #41 | semidirect |
| 116. C2×C4×C8 | D29 | semidirect |
| 147. C29 | #3167 | semidirect |
| 195. C2×C4 | #90773 | semidirect |
| 203. C8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271713 | 2 |
| #14271561 | 2 |
| #14271536 | 2 |
| #14271514 | 2 |
| #14271510 | 2 |
| #14271392 | 2 |
| C4×#90773 | 2 |
| C2×C4×C8×C29 | 2 |
| #3167 | 29 |