Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2286 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 443 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. C2×#16863264 | C2 | semidirect |
| 3. #22558433 | C2 | semidirect |
| 5. C2×#383×C67 | C2 | semidirect |
| 11. C2×C42×D67 | C4 | semidirect |
| 68. C42×C67 | C22⋊C4 | semidirect |
| 109. C2×D67 | #383 | semidirect |
| 123. C2×#383 | D67 | semidirect |
| 126. C67 | #14683 | semidirect |
| 189. C42 | (C2×D67)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D67 | 2 |
| C2×#16863264 | 2 |
| #22558433 | 2 |
| (C2×D67)⋊#95 | 2 |
| C2×#383×C67 | 2 |
| #14683 | 67 |