Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
742 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22570967 | C2 | semidirect |
| 2. #22569469 | C2 | semidirect |
| 4. #22558572 | C2 | semidirect |
| 5. #22558568 | C2 | semidirect |
| 6. #22558086 | C2 | semidirect |
| 7. C67×#1780 | C2 | semidirect |
| 250. #1780 | D67 | semidirect |
| 254. C67 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570967 | 2 |
| #22569469 | 2 |
| #22569461 | 2 |
| #22558572 | 2 |
| #22558568 | 2 |
| #22558086 | 2 |
| C67×#1780 | 2 |
| #9975 | 67 |