Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14545205 | C2 | semidirect |
| 2. C2×#11763735 | C2 | semidirect |
| 3. #14543934 | C2 | semidirect |
| 4. #14543933 | C2 | semidirect |
| 13. #11763242 | C4 | semidirect |
| 14. #11763241 | C4 | semidirect |
| 17. #11763238 | C4 | semidirect |
| 22. C17×#508 | C4 | semidirect |
| 37. C17×Q32 | C2×C4 | semidirect |
| 39. C17×D16 | C2×C4 | semidirect |
| 46. Dic136 | C2×C4 | semidirect |
| 48. D272 | C2×C4 | semidirect |
| 145. #508 | #595 | semidirect |
| 177. Q32 | C2×#595 | semidirect |
| 184. D16 | C2×#595 | semidirect |
| 194. C17 | #13616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545205 | 2 |
| C2×#11763735 | 2 |
| #14543934 | 2 |
| #14543933 | 2 |
| D17×#508 | 2 |
| #13616 | 17 |