Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 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 |
|---|---|---|
| 2. #11763227 | C2 | semidirect |
| 3. #11763226 | C2 | semidirect |
| 4. #11763225 | C2 | semidirect |
| 5. M32×D17 | C2 | semidirect |
| 6. C2×C16×D17 | C2 | semidirect |
| 7. C17×#504 | C2 | semidirect |
| 15. C17×M32 | C22 | semidirect |
| 16. C2×C16×C17 | C22 | semidirect |
| 17. #10587483 | C22 | semidirect |
| 18. C2×#63214 | C22 | semidirect |
| 19. #10587469 | C22 | semidirect |
| 22. C16×D17 | C22 | semidirect |
| 23. C16×D17 | C22 | semidirect |
| 73. #504 | D17 | direct (N × H) |
| 79. D17 | #504 | direct (N × H) |
| 89. M32 | C2×D17 | semidirect |
| 95. C2×C16 | C2×D17 | semidirect |
| 96. C17 | C2×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D17 | 2 |
| #11763227 | 2 |
| #11763226 | 2 |
| #11763225 | 2 |
| M32×D17 | 2 |
| C2×C16×D17 | 2 |
| C17×#504 | 2 |
| C2×#504 | 17 |