Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22560334 | C2 | semidirect |
| 4. #22558324 | C2 | semidirect |
| 5. #22558320 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 136. C67 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561925 | 2 |
| #22561120 | 2 |
| #22560334 | 2 |
| #22558324 | 2 |
| #22558320 | 2 |
| #22558294 | 2 |
| C2×#361×C67 | 2 |
| #13490 | 67 |