Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 2. #22558806 | C2 | semidirect |
| 3. #22558643 | C2 | semidirect |
| 4. #22558562 | C2 | semidirect |
| 5. #22558119 | C2 | semidirect |
| 6. #22558099 | C2 | semidirect |
| 7. C67×#2970 | C2 | semidirect |
| 209. #2970 | D67 | semidirect |
| 215. C67 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569703 | 2 |
| #22558806 | 2 |
| #22558643 | 2 |
| #22558562 | 2 |
| #22558119 | 2 |
| #22558099 | 2 |
| C67×#2970 | 2 |
| #9349 | 67 |