Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 474 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. C2×#16863201 | C2 | semidirect |
| 4. #22561122 | C2 | semidirect |
| 5. #22558319 | C2 | semidirect |
| 6. #22558297 | C2 | semidirect |
| 11. #16863836 | C4 | semidirect |
| 34. C2×Dic268 | C2×C4 | semidirect |
| 46. #14523983 | C2×C4 | semidirect |
| 189. C67 | #13023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863836 | 2 |
| #22569085 | 2 |
| C2×#16863201 | 2 |
| #22561122 | 2 |
| #22558319 | 2 |
| #22558297 | 2 |
| C2×#359×C67 | 2 |
| #13023 | 67 |