Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
822 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. #22558336 | C2 | semidirect |
| 4. #22558335 | C2 | semidirect |
| 5. C67×#1394 | C2 | semidirect |
| 11. #16863379 | C4 | semidirect |
| 48. #14523962 | C2×C4 | semidirect |
| 56. #101×C67 | C2×C4 | semidirect |
| 205. #1394 | D67 | semidirect |
| 206. C67 | #12585 | semidirect |
| 255. #101 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863379 | 2 |
| #22562698 | 2 |
| #22558336 | 2 |
| #22558335 | 2 |
| C67×#1394 | 2 |
| #12585 | 67 |