Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
532 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16863837 | C2 | semidirect |
| 3. C2×#16863202 | C2 | semidirect |
| 4. C2×#16863200 | C2 | semidirect |
| 5. C2×#16863180 | C2 | semidirect |
| 6. #22558319 | C2 | semidirect |
| 7. C2×#473×C67 | C2 | semidirect |
| 48. #14523983 | D4 | semidirect |
| 67. C2×Q16×C67 | D4 | semidirect |
| 79. #108×C67 | D4 | semidirect |
| 213. C2×#473 | D67 | semidirect |
| 219. C67 | #13308 | semidirect |
| 259. C2×Q16 | C22⋊D67 | semidirect |
| 287. #108 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863837 | 2 |
| #22569879 | 2 |
| C2×#16863202 | 2 |
| C2×#16863200 | 2 |
| C2×#16863180 | 2 |
| #22558319 | 2 |
| C2×#473×C67 | 2 |
| #13308 | 67 |