Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561808 | C2 | semidirect |
| 4. #22561000 | C2 | semidirect |
| 5. #22558324 | C2 | semidirect |
| 6. #22558306 | C2 | semidirect |
| 23. #362×C67 | C4 | semidirect |
| 24. #361×C67 | C4 | semidirect |
| 148. C67 | #13146 | semidirect |
| 159. #362 | Dic67 | semidirect |
| 160. #361 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863203 | 2 |
| #22561808 | 2 |
| #22561108 | 2 |
| #22561000 | 2 |
| #22558324 | 2 |
| #22558306 | 2 |
| C67×#2148 | 2 |
| #13146 | 67 |