Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22573311 | C2 | semidirect |
| 3. #22561946 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22560252 | C2 | semidirect |
| 6. #22558316 | C2 | semidirect |
| 7. C67×#1386 | C2 | semidirect |
| 15. #16863655 | C4 | semidirect |
| 16. #16863650 | C4 | semidirect |
| 50. #14523983 | D4 | semidirect |
| 63. M32×C67 | D4 | semidirect |
| 188. #1386 | D67 | semidirect |
| 189. C67 | #13077 | semidirect |
| 238. M32 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| #22569872 | 2 |
| #22561946 | 2 |
| #22561944 | 2 |
| #22560252 | 2 |
| #22558316 | 2 |
| C67×#1386 | 2 |
| #13077 | 67 |