Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
| 2. #22562042 | C2 | semidirect |
| 3. #22559575 | C2 | semidirect |
| 5. #22558257 | C2 | semidirect |
| 6. #22558254 | C2 | semidirect |
| 7. C67×#1371 | C2 | semidirect |
| 73. C16×C67 | D8 | semidirect |
| 122. #1371 | D67 | semidirect |
| 125. C67 | #12435 | semidirect |
| 191. C16 | D536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562465 | 2 |
| #22562042 | 2 |
| #22559575 | 2 |
| #22559565 | 2 |
| #22558257 | 2 |
| #22558254 | 2 |
| C67×#1371 | 2 |
| #12435 | 67 |