Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #22558281 | C2 | semidirect |
| 5. #22558267 | C2 | semidirect |
| 6. #22558264 | C2 | semidirect |
| 7. C67×#2254 | C2 | semidirect |
| 65. C16×C67 | SD16 | semidirect |
| 103. #2254 | D67 | semidirect |
| 110. C67 | #12456 | semidirect |
| 168. C16 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562042 | 2 |
| #22559605 | 2 |
| #22559595 | 2 |
| #22558281 | 2 |
| #22558267 | 2 |
| #22558264 | 2 |
| C67×#2254 | 2 |
| #12456 | 67 |