Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22571592 | C2 | semidirect |
| 3. #22561050 | C2 | semidirect |
| 4. #22558800 | C2 | semidirect |
| 5. #22558630 | C2 | semidirect |
| 6. #22558099 | C2 | semidirect |
| 7. C67×#3138 | C2 | semidirect |
| 195. #3138 | D67 | semidirect |
| 200. C67 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571592 | 2 |
| #22571127 | 2 |
| #22561050 | 2 |
| #22558800 | 2 |
| #22558630 | 2 |
| #22558099 | 2 |
| C67×#3138 | 2 |
| #10112 | 67 |