Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
496 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545094 | C2 | semidirect |
| 4. #14544946 | C2 | semidirect |
| 5. #14543846 | C2 | semidirect |
| 6. #14543837 | C2 | semidirect |
| 22. C2×#10587471 | C4 | semidirect |
| 23. C2×#10587498 | C4 | semidirect |
| 24. C2×#10587499 | C4 | semidirect |
| 28. C2×C17×SD32 | C4 | semidirect |
| 38. C2×Q16×C17 | C2×C4 | semidirect |
| 50. C2×Dic68 | C2×C4 | semidirect |
| 66. C2×C16×C17 | C2×C4 | semidirect |
| 69. C2×#63214 | C2×C4 | semidirect |
| 196. C2×SD32 | #595 | semidirect |
| 223. C2×Q16 | C2×#595 | semidirect |
| 249. C2×C16 | C2×#595 | semidirect |
| 259. C17 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545543 | 2 |
| D17⋊#361 | 2 |
| #14545094 | 2 |
| #14544946 | 2 |
| #14543846 | 2 |
| #14543837 | 2 |
| C2×SD32×D17 | 2 |
| #13019 | 17 |