Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22573312 | C2 | semidirect |
| 3. #22561924 | C2 | semidirect |
| 4. #22558310 | C2 | semidirect |
| 5. C67×#1812 | C2 | semidirect |
| 11. #16863649 | C4 | semidirect |
| 34. C2×C67⋊C16 | D4 | semidirect |
| 130. #1812 | D67 | semidirect |
| 132. C67 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573312 | 2 |
| #22569857 | 2 |
| #22561924 | 2 |
| #22558310 | 2 |
| C67×#1812 | 2 |
| #13074 | 67 |