Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22569060 | C2 | semidirect |
| 3. C2×#16863208 | C2 | semidirect |
| 4. #22561924 | C2 | semidirect |
| 5. #22561117 | C2 | semidirect |
| 6. #22558297 | C2 | semidirect |
| 7. C67×#1382 | C2 | semidirect |
| 13. C2×D1072 | C4 | semidirect |
| 37. C2×D536 | C2×C4 | semidirect |
| 59. C2×C16×C67 | C2×C4 | semidirect |
| 171. #1382 | D67 | semidirect |
| 173. C67 | #13017 | semidirect |
| 220. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| #22569060 | 2 |
| C2×#16863208 | 2 |
| #22561924 | 2 |
| #22561117 | 2 |
| #22558297 | 2 |
| C67×#1382 | 2 |
| #13017 | 67 |