Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
| 2. #14271463 | C2 | semidirect |
| 3. #14271453 | C2 | semidirect |
| 4. #14271443 | C2 | semidirect |
| 5. #14271203 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 22. #11745232 | C22 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. #11745231 | C22 | semidirect |
| 29. #11745156 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 36. C2×D4×C29 | Q8 | semidirect |
| 148. C29 | #3077 | semidirect |
| 154. C2×D4 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271463 | 2 |
| #14271453 | 2 |
| #14271443 | 2 |
| #14271203 | 2 |
| #14271187 | 2 |
| #14271168 | 2 |
| C2×C4×D4×C29 | 2 |
| #3077 | 29 |