Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1958 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1958 conjugacy classes of subgroups — too many to draw. Only its 587 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. #22568395 | C2 | direct (N × H) |
| 2. C2×C67⋊#401 | C2 | semidirect |
| 3. C2×#16863329 | C2 | semidirect |
| 11. C67⋊#401 | C22 | semidirect |
| 12. #16863329 | C22 | semidirect |
| 106. C2×C67 | #2834 | semidirect |
| 116. C67 | C2×#2834 | semidirect |
| 215. C2 | #22568395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568395 | 2 |
| C2×C67⋊#401 | 2 |
| C2×#16863329 | 2 |
| C2×#16863321 | 2 |
| C2×#16863268 | 2 |
| C2×#399×C67 | 2 |
| C2×#2834 | 67 |