Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562491 | C2 | semidirect |
| 4. #22558281 | C2 | semidirect |
| 5. #22558266 | C2 | semidirect |
| 6. #22558263 | C2 | semidirect |
| 65. C16×C67 | SD16 | semidirect |
| 110. C67 | #12456 | semidirect |
| 168. C16 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562491 | 2 |
| #22559608 | 2 |
| #22559598 | 2 |
| #22558281 | 2 |
| #22558266 | 2 |
| #22558263 | 2 |
| C67×#2169 | 2 |
| #12456 | 67 |