Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562362 | C2 | semidirect |
| 4. #22559107 | C2 | semidirect |
| 5. #22558266 | C2 | semidirect |
| 7. C67×#1370 | C2 | semidirect |
| 113. #1370 | D67 | semidirect |
| 116. C67 | #12486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562362 | 2 |
| #22562250 | 2 |
| #22559801 | 2 |
| #22559107 | 2 |
| #22558266 | 2 |
| #22558256 | 2 |
| C67×#1370 | 2 |
| #12486 | 67 |