Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
634 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22560277 | C2 | semidirect |
| 3. #22558029 | C2 | semidirect |
| 4. C67×#1797 | C2 | semidirect |
| 184. #1797 | D67 | semidirect |
| 186. C67 | #7724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568554 | 2 |
| #22560277 | 2 |
| #22558029 | 2 |
| C67×#1797 | 2 |
| #7724 | 67 |