Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22568806 | C2 | semidirect |
| 3. #22561924 | C2 | semidirect |
| 4. C2×#16863198 | C2 | semidirect |
| 5. C2×#16863179 | C2 | semidirect |
| 6. #22558319 | C2 | semidirect |
| 7. C67×#1382 | C2 | semidirect |
| 14. #16863667 | C4 | semidirect |
| 39. C2×D536 | C2×C4 | semidirect |
| 68. #108×C67 | C2×C4 | semidirect |
| 195. #1382 | D67 | semidirect |
| 196. C67 | #12996 | semidirect |
| 252. #108 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863667 | 2 |
| #22568806 | 2 |
| #22561924 | 2 |
| C2×#16863198 | 2 |
| C2×#16863179 | 2 |
| #22558319 | 2 |
| C67×#1382 | 2 |
| #12996 | 67 |