Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
496 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22561930 | C2 | semidirect |
| 4. #22561122 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 12. C2×#14523987 | C4 | semidirect |
| 32. C2×Dic268 | C2×C4 | semidirect |
| 42. C2×C67⋊C16 | C2×C4 | semidirect |
| 168. C67 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523987 | 2 |
| #22569061 | 2 |
| #22561930 | 2 |
| #22561122 | 2 |
| #22558306 | 2 |
| #22558299 | 2 |
| C2×#361×C67 | 2 |
| #13019 | 67 |