Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14271961 | C2 | semidirect |
| 2. C2×#11745311 | C2 | semidirect |
| 3. #14271732 | C2 | semidirect |
| 4. #14271181 | C2 | semidirect |
| 5. #14271167 | C2 | semidirect |
| 6. #14270933 | C2 | semidirect |
| 7. C29×#410 | C2 | semidirect |
| 36. C2×Q8×C29 | D4 | semidirect |
| 38. C2×D4×C29 | D4 | semidirect |
| 72. #90777 | D4 | semidirect |
| 74. C2×#6597 | D4 | semidirect |
| 141. #410 | D29 | semidirect |
| 173. C29 | #2008 | semidirect |
| 184. C2×Q8 | D116 | semidirect |
| 195. C2×D4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| C2×#11745311 | 2 |
| #14271732 | 2 |
| #14271181 | 2 |
| #14271167 | 2 |
| #14270933 | 2 |
| C29×#410 | 2 |
| #2008 | 29 |