Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D1072 | C2 | semidirect |
| 2. C2×#16863812 | C2 | semidirect |
| 3. #22569858 | C2 | semidirect |
| 4. #22562313 | C2 | semidirect |
| 5. #22562296 | C2 | semidirect |
| 6. #22561924 | C2 | semidirect |
| 7. C67×#2158 | C2 | semidirect |
| 16. C2×#14523982 | C22 | semidirect |
| 17. C2×C16×D67 | C22 | semidirect |
| 19. #16863633 | C22 | semidirect |
| 21. #16863196 | C22 | semidirect |
| 24. #367×C67 | C22 | semidirect |
| 25. #366×C67 | C22 | semidirect |
| 50. C2×C16×C67 | D4 | semidirect |
| 135. #2158 | D67 | semidirect |
| 137. C67 | #33607 | semidirect |
| 153. #367 | C2×D67 | semidirect |
| 154. #366 | C2×D67 | semidirect |
| 179. C2×C16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| C2×#16863812 | 2 |
| #22569858 | 2 |
| #22562313 | 2 |
| #22562296 | 2 |
| #22561924 | 2 |
| C67×#2158 | 2 |
| #33607 | 67 |