Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
514 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16863193 | C2 | semidirect |
| 2. C2×#16863136 | C2 | semidirect |
| 3. #22558357 | C2 | direct (N × H) |
| 8. #16863193 | C22 | semidirect |
| 10. #16863136 | C22 | semidirect |
| 177. C2×C67 | #1403 | semidirect |
| 183. C67 | C2×#1403 | semidirect |
| 355. C2 | #22558357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863193 | 2 |
| C2×#16863136 | 2 |
| #22558357 | 2 |
| C2×#455×C67 | 2 |
| C2×#1403 | 67 |