Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 2. #22562003 | C2 | semidirect |
| 3. C2×#16863226 | C2 | semidirect |
| 6. #22558325 | C2 | semidirect |
| 7. C67×#1382 | C2 | semidirect |
| 19. #16863179 | C4 | semidirect |
| 144. #1382 | D67 | semidirect |
| 145. C67 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568817 | 2 |
| #22562003 | 2 |
| C2×#16863226 | 2 |
| C2×#16863179 | 2 |
| #22560260 | 2 |
| #22558325 | 2 |
| C67×#1382 | 2 |
| #12927 | 67 |