Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 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 |
|---|---|---|
| 1. #22571339 | C2 | semidirect |
| 2. #22571136 | C2 | semidirect |
| 4. #22561182 | C2 | semidirect |
| 5. #22558770 | C2 | semidirect |
| 6. #22558770 | C2 | semidirect |
| 7. C67×#1281 | C2 | semidirect |
| 123. C2×C8×C67 | SD16 | semidirect |
| 202. #1281 | D67 | semidirect |
| 203. C67 | #10221 | semidirect |
| 306. C2×C8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571339 | 2 |
| #22571136 | 2 |
| #22570655 | 2 |
| #22561182 | 2 |
| #22558770 | 2 |
| C67×#1281 | 2 |
| #10221 | 67 |