Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
508 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22571204 | C2 | semidirect |
| 2. #22571200 | C2 | semidirect |
| 3. #22558757 | C2 | semidirect |
| 4. #22558756 | C2 | semidirect |
| 5. #22558756 | C2 | semidirect |
| 6. C67⋊#1308 | C2 | semidirect |
| 7. C67×#3214 | C2 | semidirect |
| 208. #3214 | D67 | semidirect |
| 213. C67 | #10208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571204 | 2 |
| #22571200 | 2 |
| #22558757 | 2 |
| #22558756 | 2 |
| C67⋊#1308 | 2 |
| C67×#3214 | 2 |
| #10208 | 67 |