Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22571407 | C2 | semidirect |
| 3. #22558677 | C2 | semidirect |
| 4. #22558630 | C2 | semidirect |
| 5. #22558561 | C2 | semidirect |
| 6. #22558080 | C2 | semidirect |
| 7. C67×#3215 | C2 | semidirect |
| 203. #3215 | D67 | semidirect |
| 209. C67 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571407 | 2 |
| #22570673 | 2 |
| #22558677 | 2 |
| #22558630 | 2 |
| #22558561 | 2 |
| #22558080 | 2 |
| C67×#3215 | 2 |
| #10121 | 67 |