Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22571159 | C2 | semidirect |
| 4. #22558895 | C2 | semidirect |
| 5. #22558611 | C2 | semidirect |
| 7. C67×#1301 | C2 | semidirect |
| 86. C2×D268 | Q16 | semidirect |
| 197. #1301 | D67 | semidirect |
| 198. C67 | #10182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571159 | 2 |
| #22570008 | 2 |
| C2×#16863687 | 2 |
| #22558895 | 2 |
| #22558611 | 2 |
| #22558529 | 2 |
| C67×#1301 | 2 |
| #10182 | 67 |