Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22562008 | C2 | semidirect |
| 2. #22558972 | C2 | semidirect |
| 3. #22558252 | C2 | semidirect |
| 6. C4⋊(C67⋊C16) | C22 | semidirect |
| 10. #16863147 | C22 | semidirect |
| 137. C67 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562008 | 2 |
| #22558972 | 2 |
| #22558252 | 2 |
| C2×#495×C67 | 2 |
| #11957 | 67 |