Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22561048 | C2 | semidirect |
| 3. #22559000 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558626 | C2 | semidirect |
| 6. #22558098 | C2 | semidirect |
| 7. C67×#1560 | C2 | semidirect |
| 176. #1560 | D67 | semidirect |
| 180. C67 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22561048 | 2 |
| #22559000 | 2 |
| #22558878 | 2 |
| #22558626 | 2 |
| #22558098 | 2 |
| C67×#1560 | 2 |
| #10488 | 67 |