Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16863668 | C2 | semidirect |
| 3. C2×#16863203 | C2 | semidirect |
| 4. C2×#16863200 | C2 | semidirect |
| 5. C2×#16863181 | C2 | semidirect |
| 6. #22558318 | C2 | semidirect |
| 7. C2×#510×C67 | C2 | semidirect |
| 54. #14523979 | D4 | semidirect |
| 72. C2×Q16×C67 | D4 | semidirect |
| 79. M32×C67 | D4 | semidirect |
| 212. C2×#510 | D67 | semidirect |
| 219. C67 | #13308 | semidirect |
| 259. C2×Q16 | C22⋊D67 | semidirect |
| 281. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863668 | 2 |
| #22569875 | 2 |
| C2×#16863203 | 2 |
| C2×#16863200 | 2 |
| C2×#16863181 | 2 |
| #22558318 | 2 |
| C2×#510×C67 | 2 |
| #13308 | 67 |