Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561901 | C2 | semidirect |
| 2. #22561859 | C2 | semidirect |
| 3. #22560259 | C2 | semidirect |
| 4. #22560009 | C2 | semidirect |
| 15. C22×D8×C67 | C4 | semidirect |
| 22. #427×C67 | C4 | semidirect |
| 23. #418×C67 | C4 | semidirect |
| 172. C67 | #13234 | semidirect |
| 173. C22×D8 | Dic67 | semidirect |
| 181. #427 | Dic67 | semidirect |
| 182. #418 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561901 | 2 |
| #22561859 | 2 |
| #22560259 | 2 |
| #22560009 | 2 |
| C67×#3058 | 2 |
| #13234 | 67 |