Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 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 |
|---|---|---|
| 3. #22559027 | C2 | semidirect |
| 4. #22558178 | C2 | semidirect |
| 6. #22558131 | C2 | semidirect |
| 7. C67×#1368 | C2 | semidirect |
| 48. Dic268 | M16 | semidirect |
| 106. #1368 | D67 | semidirect |
| 110. C67 | #12080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562075 | 2 |
| #22559122 | 2 |
| #22559027 | 2 |
| #22558178 | 2 |
| #22558175 | 2 |
| #22558131 | 2 |
| C67×#1368 | 2 |
| #12080 | 67 |