Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 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. #22560328 | C2 | semidirect |
| 3. #22558985 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1570 | C2 | semidirect |
| 132. #1570 | D67 | semidirect |
| 136. C67 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561040 | 2 |
| #22560328 | 2 |
| #22558985 | 2 |
| #22558609 | 2 |
| #22558607 | 2 |
| #22558037 | 2 |
| C67×#1570 | 2 |
| #10665 | 67 |