Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #22558273 | C2 | semidirect |
| 5. #22558267 | C2 | semidirect |
| 6. #22558258 | C2 | semidirect |
| 7. C67×#1707 | C2 | semidirect |
| 87. C8×C67 | SD32 | semidirect |
| 110. #1707 | D67 | semidirect |
| 115. C67 | #12420 | semidirect |
| 196. C8 | #14523986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562353 | 2 |
| #22562251 | 2 |
| C8×D536 | 2 |
| #22558273 | 2 |
| #22558267 | 2 |
| #22558258 | 2 |
| C67×#1707 | 2 |
| #12420 | 67 |