Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22565699 | C2 | semidirect |
| 3. #22559246 | C2 | semidirect |
| 4. #22558237 | C2 | semidirect |
| 5. #22558215 | C2 | semidirect |
| 6. #22558140 | C2 | semidirect |
| 7. C67×#1610 | C2 | semidirect |
| 198. #1610 | D67 | semidirect |
| 202. C67 | #12196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22565699 | 2 |
| #22561251 | 2 |
| #22559246 | 2 |
| #22558237 | 2 |
| #22558215 | 2 |
| #22558140 | 2 |
| C67×#1610 | 2 |
| #12196 | 67 |