Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562395 | C2 | semidirect |
| 3. #22562392 | C2 | semidirect |
| 4. #22561704 | C2 | semidirect |
| 5. #22558217 | C2 | semidirect |
| 6. #22558148 | C2 | semidirect |
| 7. C67×#1347 | C2 | semidirect |
| 169. #1347 | D67 | semidirect |
| 171. C67 | #12291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571515 | 2 |
| #22562395 | 2 |
| #22562392 | 2 |
| #22561704 | 2 |
| #22558217 | 2 |
| #22558148 | 2 |
| C67×#1347 | 2 |
| #12291 | 67 |