Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #22560378 | C2 | semidirect |
| 4. #22560377 | C2 | semidirect |
| 6. #22558091 | C2 | semidirect |
| 7. C67×#1295 | C2 | semidirect |
| 24. #16863135 | C4 | semidirect |
| 55. #14523954 | C2×C4 | semidirect |
| 68. #97×C67 | C2×C4 | semidirect |
| 211. #1295 | D67 | semidirect |
| 212. C67 | #8910 | semidirect |
| 269. #97 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563380 | 2 |
| #22561025 | 2 |
| #22560378 | 2 |
| #22560377 | 2 |
| C2×#16863135 | 2 |
| #22558091 | 2 |
| C67×#1295 | 2 |
| #8910 | 67 |