Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 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. #22558964 | C2 | semidirect |
| 3. #22558887 | C2 | semidirect |
| 4. #22558659 | C2 | semidirect |
| 5. C2×D4⋊(C67⋊C8) | C2 | semidirect |
| 6. #22558083 | C2 | semidirect |
| 7. C67×#1800 | C2 | semidirect |
| 202. #1800 | D67 | semidirect |
| 208. C67 | #10457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569673 | 2 |
| #22558964 | 2 |
| #22558887 | 2 |
| #22558659 | 2 |
| C2×D4⋊(C67⋊C8) | 2 |
| #22558083 | 2 |
| C67×#1800 | 2 |
| #10457 | 67 |