Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
482 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. #22562860 | C2 | semidirect |
| 4. #22558656 | C2 | semidirect |
| 5. #22558101 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 24. #477×C67 | C4 | semidirect |
| 25. #460×C67 | C4 | semidirect |
| 188. C67 | #9330 | semidirect |
| 192. #477 | Dic67 | semidirect |
| 193. #460 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562860 | 2 |
| #22561129 | 2 |
| #22558717 | 2 |
| #22558656 | 2 |
| #22558101 | 2 |
| #22558066 | 2 |
| C67×#3112 | 2 |
| #9330 | 67 |