Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271631 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. C2×#11745185 | C2 | semidirect |
| 5. #14270933 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#410 | C2 | semidirect |
| 15. #11745304 | C4 | semidirect |
| 16. #11745294 | C4 | semidirect |
| 33. C2×Q8×C29 | C2×C4 | semidirect |
| 35. C2×D4×C29 | C2×C4 | semidirect |
| 67. #90777 | C2×C4 | semidirect |
| 128. #410 | D29 | semidirect |
| 158. C29 | #1906 | semidirect |
| 168. C2×Q8 | C4×D29 | semidirect |
| 172. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| #14271631 | 2 |
| #14271181 | 2 |
| C2×#11745185 | 2 |
| #14270933 | 2 |
| #14270922 | 2 |
| C29×#410 | 2 |
| #1906 | 29 |