Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
534 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 534 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. #14544208 | C2 | semidirect |
| 4. #14544207 | C2 | semidirect |
| 5. #14543644 | C2 | semidirect |
| 6. #14543644 | C2 | semidirect |
| 21. #11763157 | C4 | semidirect |
| 22. #11763156 | C4 | semidirect |
| 23. #11763155 | C4 | semidirect |
| 26. C17×#486 | C4 | semidirect |
| 34. C17×C4⋊Q8 | C2×C4 | semidirect |
| 48. #10587555 | C2×C4 | semidirect |
| 62. C4×C8×C17 | C2×C4 | semidirect |
| 67. C4×#3622 | C2×C4 | semidirect |
| 194. #486 | #595 | semidirect |
| 219. C4⋊Q8 | C2×#595 | semidirect |
| 247. C4×C8 | C2×#595 | semidirect |
| 254. C17 | #9425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545328 | 2 |
| #14544312 | 2 |
| #14544208 | 2 |
| #14544207 | 2 |
| #14543644 | 2 |
| #14539155 | 2 |
| #9425 | 17 |