Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22568928 | C2 | semidirect |
| 3. #22558877 | C2 | semidirect |
| 4. #22558768 | C2 | semidirect |
| 5. #22558067 | C2 | semidirect |
| 6. #22558040 | C2 | semidirect |
| 7. C67×#1961 | C2 | semidirect |
| 10. #16863772 | C4 | semidirect |
| 11. #16863742 | C4 | semidirect |
| 112. C2×C8×C67 | D8 | semidirect |
| 198. #1961 | D67 | semidirect |
| 203. C67 | #9293 | semidirect |
| 304. C2×C8 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571127 | 2 |
| #22568928 | 2 |
| #22558877 | 2 |
| #22558768 | 2 |
| #22558067 | 2 |
| #22558040 | 2 |
| C67×#1961 | 2 |
| #9293 | 67 |