Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22562004 | C2 | semidirect |
| 4. #22561000 | C2 | semidirect |
| 5. #22558302 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 23. #362×C67 | C4 | semidirect |
| 24. #361×C67 | C4 | semidirect |
| 149. C67 | #12942 | semidirect |
| 163. #362 | Dic67 | semidirect |
| 164. #361 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569126 | 2 |
| #22562004 | 2 |
| C2×#16863203 | 2 |
| #22561000 | 2 |
| #22558302 | 2 |
| #22558299 | 2 |
| C67×#2148 | 2 |
| #12942 | 67 |