Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
| 5. #22558101 | C2 | semidirect |
| 6. #22558058 | C2 | semidirect |
| 7. C67×#1573 | C2 | semidirect |
| 179. #1573 | D67 | semidirect |
| 184. C67 | #8877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569350 | 2 |
| #22560328 | 2 |
| #22558696 | 2 |
| #22558620 | 2 |
| #22558101 | 2 |
| #22558058 | 2 |
| C67×#1573 | 2 |
| #8877 | 67 |