Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
926 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22571407 | C2 | semidirect |
| 3. #22559520 | C2 | semidirect |
| 4. #22559507 | C2 | semidirect |
| 5. #22558844 | C2 | semidirect |
| 6. #22558824 | C2 | semidirect |
| 7. C67×#3550 | C2 | semidirect |
| 176. #3550 | D67 | semidirect |
| 183. C67 | #19054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571407 | 2 |
| #22570654 | 2 |
| #22559520 | 2 |
| #22559507 | 2 |
| #22558844 | 2 |
| #22558824 | 2 |
| C67×#3550 | 2 |
| #19054 | 67 |