Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22570745 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 7. C67×#1387 | C2 | semidirect |
| 31. C2×D536 | Q8 | semidirect |
| 163. #1387 | D67 | semidirect |
| 166. C67 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570745 | 2 |
| #22561926 | 2 |
| C2×#16863196 | 2 |
| #22561117 | 2 |
| #22558306 | 2 |
| #22558299 | 2 |
| C67×#1387 | 2 |
| #13369 | 67 |