Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
790 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 18. #11762566 | C4 | semidirect |
| 19. #11762565 | C4 | semidirect |
| 20. C17×H(3,ℤ/4) | C4 | semidirect |
| 89. C2×C8×C17 | C4⋊C4 | semidirect |
| 92. C42×C17 | C4⋊C4 | semidirect |
| 98. C4×Dic17 | C4⋊C4 | semidirect |
| 100. C2×#3622 | C4⋊C4 | semidirect |
| 180. H(3,ℤ/4) | #595 | semidirect |
| 224. C17 | #11335 | semidirect |
| 252. C2×C8 | C4⋊#595 | semidirect |
| 271. C42 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545437 | 2 |
| #14545244 | 2 |
| #14544465 | 2 |
| #14544446 | 2 |
| D17×H(3,ℤ/4) | 2 |
| #11335 | 17 |