Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #14271598 | C2 | semidirect |
| 2. #14271540 | C2 | semidirect |
| 3. #14270984 | C2 | semidirect |
| 4. #14270975 | C2 | semidirect |
| 5. C29×#443 | C2 | semidirect |
| 20. Q16×C29 | D4 | semidirect |
| 22. D8×C29 | D4 | semidirect |
| 60. #443 | D29 | semidirect |
| 78. C29 | #2213 | semidirect |
| 82. Q16 | D116 | semidirect |
| 88. D8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271598 | 2 |
| #14271540 | 2 |
| #14270984 | 2 |
| #14270975 | 2 |
| C29×#443 | 2 |
| #2213 | 29 |