Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
626 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22572921 | C2 | semidirect |
| 2. #22572546 | C2 | semidirect |
| 3. #22559746 | C2 | semidirect |
| 4. #22559739 | C2 | semidirect |
| 5. #22559340 | C2 | semidirect |
| 6. #22559271 | C2 | semidirect |
| 7. #22559107 | C2 | semidirect |
| 8. #22559095 | C2 | semidirect |
| 9. C67×#1709 | C2 | semidirect |
| 177. #1709 | D67 | semidirect |
| 184. C67 | #20308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572921 | 2 |
| #22572546 | 2 |
| #22559746 | 2 |
| #22559739 | 2 |
| #22559340 | 2 |
| #22559271 | 2 |
| #22559107 | 2 |
| #22559095 | 2 |
| C67×#1709 | 2 |
| #20308 | 67 |