Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22562143 | C2 | semidirect |
| 4. #22562126 | C2 | semidirect |
| 5. #22561929 | C2 | semidirect |
| 6. #22561820 | C2 | semidirect |
| 7. C23×Q16×C67 | C2 | semidirect |
| 11. C2×#14523989 | C22 | semidirect |
| 12. C2×#14523986 | C22 | semidirect |
| 19. #16863200 | C22 | semidirect |
| 61. C2×Q16×C67 | D4 | semidirect |
| 153. C22×C67 | #510 | semidirect |
| 170. C23×Q16 | D67 | semidirect |
| 177. C67 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D67 | semidirect |
| 325. C22 | #16863837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863837 | 2 |
| #22569790 | 2 |
| #22562143 | 2 |
| #22562126 | 2 |
| #22561929 | 2 |
| #22561820 | 2 |
| C23×Q16×C67 | 2 |
| #33518 | 67 |