Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 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. #22562465 | C2 | semidirect |
| 3. #22562437 | C2 | semidirect |
| 4. #22562433 | C2 | semidirect |
| 5. #22559815 | C2 | semidirect |
| 6. #22559801 | C2 | semidirect |
| 7. C67×#1312 | C2 | semidirect |
| 119. #1312 | D67 | semidirect |
| 120. C67 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562465 | 2 |
| #22562459 | 2 |
| #22562437 | 2 |
| #22562433 | 2 |
| #22559815 | 2 |
| #22559801 | 2 |
| C67×#1312 | 2 |
| #12527 | 67 |