Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22569120 | C2 | semidirect |
| 2. #22562421 | C2 | semidirect |
| 3. #22562377 | C2 | semidirect |
| 4. #22562282 | C2 | semidirect |
| 5. #22562154 | C2 | semidirect |
| 6. #22562105 | C2 | semidirect |
| 7. #22562021 | C2 | semidirect |
| 8. C67×#3184 | C2 | semidirect |
| 18. #16863218 | C22 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 20. #16863209 | C22 | semidirect |
| 23. #16863174 | C22 | semidirect |
| 25. #498×C67 | C22 | semidirect |
| 26. #493×C67 | C22 | semidirect |
| 31. #442×C67 | C22 | semidirect |
| 80. Dic268 | #41 | semidirect |
| 84. D536 | #41 | semidirect |
| 170. #3184 | D67 | semidirect |
| 178. C67 | #33688 | semidirect |
| 183. #498 | C2×D67 | semidirect |
| 184. #493 | C2×D67 | semidirect |
| 193. #442 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569120 | 2 |
| #22562421 | 2 |
| #22562377 | 2 |
| #22562282 | 2 |
| #22562154 | 2 |
| #22562105 | 2 |
| #22562021 | 2 |
| C67×#3184 | 2 |
| #33688 | 67 |