Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22558967 | C2 | semidirect |
| 5. C2×Q8⋊(C67⋊C8) | C2 | semidirect |
| 6. #22558083 | C2 | semidirect |
| 7. C67×#1801 | C2 | semidirect |
| 190. #1801 | D67 | semidirect |
| 196. C67 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569681 | 2 |
| #22558967 | 2 |
| #22558887 | 2 |
| #22558659 | 2 |
| C2×Q8⋊(C67⋊C8) | 2 |
| #22558083 | 2 |
| C67×#1801 | 2 |
| #10458 | 67 |