Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 2. #22562863 | C2 | semidirect |
| 3. #22560617 | C2 | semidirect |
| 4. #22560490 | C2 | semidirect |
| 5. #22560157 | C2 | semidirect |
| 6. C4×#14523958 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C67 | C2 | semidirect |
| 9. C22×(C2×D67)⋊C4 | C22 | semidirect |
| 10. #16863583 | C4 | semidirect |
| 18. #16863268 | C22 | semidirect |
| 19. #16863251 | C22 | semidirect |
| 20. C4×C22⋊Dic67 | C22 | semidirect |
| 21. #16863163 | C22 | semidirect |
| 33. #14524011 | C2×C4 | semidirect |
| 45. #14523958 | C2×C4 | semidirect |
| 55. C23×C4×C67 | D4 | semidirect |
| 69. C2×C4⋊C4×C67 | D4 | semidirect |
| 72. C2×C22⋊C4×C67 | D4 | semidirect |
| 75. C2×C42×C67 | D4 | semidirect |
| 80. C23×D67 | C22×C4 | semidirect |
| 92. C22⋊Dic67 | C22×C4 | semidirect |
| 222. C4×H(5,𝔽2) | D67 | semidirect |
| 229. C67 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D67 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D67 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D67 | semidirect |
| 292. C2×C42 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863583 | 2 |
| #22562863 | 2 |
| #22560617 | 2 |
| #22560490 | 2 |
| #22560157 | 2 |
| C4×#14523958 | 2 |
| C4×H(5,𝔽2)×C67 | 2 |
| #21482 | 67 |