Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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. #14545004 | C2 | semidirect |
| 4. #14544901 | C2 | semidirect |
| 5. #14543864 | C2 | semidirect |
| 6. #14543856 | C2 | semidirect |
| 23. #11762625 | C4 | semidirect |
| 24. #11762623 | C4 | semidirect |
| 25. #11762621 | C4 | semidirect |
| 26. C17×#362 | C4 | semidirect |
| 164. #362 | #595 | semidirect |
| 212. C17 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763726 | 2 |
| #14545004 | 2 |
| #14544943 | 2 |
| #14544901 | 2 |
| #14543864 | 2 |
| #14543856 | 2 |
| #14530532 | 2 |
| #13156 | 17 |