Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22560336 | C2 | semidirect |
| 4. C67⋊#1273 | C2 | semidirect |
| 5. C67×#1844 | C2 | semidirect |
| 111. #1844 | D67 | semidirect |
| 114. C67 | #10677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561015 | 2 |
| #22561014 | 2 |
| #22560336 | 2 |
| C67⋊#1273 | 2 |
| C67×#1844 | 2 |
| #10677 | 67 |