Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22561929 | C2 | semidirect |
| 5. #22558324 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C2×#362×C67 | C2 | semidirect |
| 15. #16863668 | C4 | semidirect |
| 164. C2×#362 | D67 | semidirect |
| 169. C67 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| C2×#16863668 | 2 |
| #22561929 | 2 |
| #22560264 | 2 |
| #22558324 | 2 |
| #22558312 | 2 |
| C2×#362×C67 | 2 |
| #13069 | 67 |