Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22562010 | C2 | semidirect |
| 3. #22558963 | C2 | semidirect |
| 4. #22558177 | C2 | semidirect |
| 5. #22558176 | C2 | semidirect |
| 6. #22558175 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 21. #16863172 | C22 | semidirect |
| 22. #16863147 | C22 | semidirect |
| 25. #346×C67 | C22 | semidirect |
| 26. #334×C67 | C22 | semidirect |
| 76. D536 | M16 | semidirect |
| 97. D8×C67 | M16 | semidirect |
| 173. #1333 | D67 | semidirect |
| 174. C67 | #11663 | semidirect |
| 190. #346 | C2×D67 | semidirect |
| 193. #334 | C2×D67 | semidirect |
| 248. D8 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D67 | 2 |
| #22562010 | 2 |
| #22558963 | 2 |
| #22558177 | 2 |
| #22558176 | 2 |
| #22558175 | 2 |
| C67×#1333 | 2 |
| #11663 | 67 |