Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 4. #22558273 | C2 | semidirect |
| 5. #22558267 | C2 | semidirect |
| 6. #22558264 | C2 | semidirect |
| 7. C67×#1710 | C2 | semidirect |
| 106. #1710 | D67 | semidirect |
| 111. C67 | #12501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562353 | 2 |
| #22562343 | 2 |
| #22559095 | 2 |
| #22558273 | 2 |
| #22558267 | 2 |
| #22558264 | 2 |
| C67×#1710 | 2 |
| #12501 | 67 |