Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22560930 | C2 | semidirect |
| 4. #22558708 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#1542 | C2 | semidirect |
| 191. #1542 | D67 | semidirect |
| 196. C67 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570557 | 2 |
| #22560930 | 2 |
| #22558859 | 2 |
| #22558708 | 2 |
| #22558705 | 2 |
| #22558039 | 2 |
| C67×#1542 | 2 |
| #10547 | 67 |