Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
360 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22561164 | C2 | semidirect |
| 5. #22558564 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1573 | C2 | semidirect |
| 172. #1573 | D67 | semidirect |
| 177. C67 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571401 | 2 |
| #22561164 | 2 |
| #22558902 | 2 |
| #22558705 | 2 |
| #22558564 | 2 |
| #22558066 | 2 |
| C67×#1573 | 2 |
| #10509 | 67 |