Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22560224 | C2 | semidirect |
| 2. #22558985 | C2 | semidirect |
| 5. #22558533 | C2 | semidirect |
| 6. #22558069 | C2 | semidirect |
| 189. C67 | #10466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560224 | 2 |
| #22558985 | 2 |
| #22558858 | 2 |
| #22558769 | 2 |
| #22558533 | 2 |
| #22558069 | 2 |
| C67×#3037 | 2 |
| #10466 | 67 |