Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 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. #14272188 | C2 | semidirect |
| 2. #14272187 | C2 | semidirect |
| 3. #14272168 | C2 | semidirect |
| 4. #14272167 | C2 | semidirect |
| 6. C4×#90796 | C2 | semidirect |
| 22. #11745220 | C22 | semidirect |
| 24. #11745218 | C22 | semidirect |
| 25. C4⋊#6599 | C22 | semidirect |
| 26. C4×#6599 | C22 | semidirect |
| 131. C29 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272188 | 2 |
| #14272187 | 2 |
| #14272168 | 2 |
| #14272167 | 2 |
| #14272134 | 2 |
| C4×#90796 | 2 |
| #117×D29 | 2 |
| #2921 | 29 |