Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1010 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16864146 | C2 | semidirect |
| 2. C2×#16863760 | C2 | semidirect |
| 3. #22559505 | C2 | direct (N × H) |
| 4. C2×#16863137 | C2 | semidirect |
| 5. C2×#16863136 | C2 | semidirect |
| 9. #16864146 | C22 | semidirect |
| 16. #16863760 | C22 | semidirect |
| 20. #16863137 | C22 | semidirect |
| 21. #16863136 | C22 | semidirect |
| 173. C2×C67 | #1657 | semidirect |
| 182. C67 | C2×#1657 | semidirect |
| 348. C2 | #22559505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864146 | 2 |
| C2×#16863760 | 2 |
| #22559505 | 2 |
| C2×#16863137 | 2 |
| C2×#16863136 | 2 |
| C2×#496×C67 | 2 |
| C2×#1657 | 67 |