Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
410 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22571099 | C2 | semidirect |
| 2. #22562138 | C2 | semidirect |
| 4. #22558228 | C2 | semidirect |
| 5. #22558227 | C2 | semidirect |
| 6. #22558134 | C2 | semidirect |
| 7. C67×#2187 | C2 | semidirect |
| 181. #2187 | D67 | semidirect |
| 186. C67 | #12109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571099 | 2 |
| #22562138 | 2 |
| #22561316 | 2 |
| #22558228 | 2 |
| #22558227 | 2 |
| #22558134 | 2 |
| C67×#2187 | 2 |
| #12109 | 67 |