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×#11763736 | C2 | semidirect |
| 3. #14543938 | C2 | semidirect |
| 4. #14543937 | C2 | semidirect |
| 7. #11763742 | C22 | semidirect |
| 11. #11763736 | C22 | semidirect |
| 14. #11763241 | C4 | semidirect |
| 18. Q32×D17 | C4 | semidirect |
| 20. D16×D17 | 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 |
| 143. #508 | #595 | semidirect |
| 159. D17 | #1418 | semidirect |
| 174. Q32 | C2×#595 | semidirect |
| 181. D16 | C2×#595 | semidirect |
| 191. C17 | C2×#1418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545205 | 2 |
| C2×#11763736 | 2 |
| #14543938 | 2 |
| #14543937 | 2 |
| D17×#508 | 2 |
| C2×#1418 | 17 |