Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
490 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #14544178 | C2 | semidirect |
| 4. #14544176 | C2 | semidirect |
| 5. #14543673 | C2 | semidirect |
| 6. #14543673 | C2 | semidirect |
| 26. #11763171 | C4 | semidirect |
| 27. #11763169 | C4 | semidirect |
| 28. #11763168 | C4 | semidirect |
| 34. C17×#489 | C4 | semidirect |
| 45. C17×C4⋊Q8 | C2×C4 | semidirect |
| 62. #10587555 | C2×C4 | semidirect |
| 79. C17×#97 | C2×C4 | semidirect |
| 87. #10587474 | C2×C4 | semidirect |
| 237. #489 | #595 | semidirect |
| 271. C4⋊Q8 | C2×#595 | semidirect |
| 309. #97 | C2×#595 | semidirect |
| 319. C17 | #9439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545320 | 2 |
| #14544264 | 2 |
| #14544178 | 2 |
| #14544176 | 2 |
| #14543673 | 2 |
| #14539169 | 2 |
| #9439 | 17 |