Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
800 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 289 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. #11763284 | C2 | semidirect |
| 2. #11762783 | C2 | semidirect |
| 3. C2×#10587505 | C2 | semidirect |
| 6. C2×#41×C17 | C4 | semidirect |
| 8. C22×D4×C17 | C4 | semidirect |
| 11. C2×C22⋊Dic17 | C22 | semidirect |
| 13. #10587612 | C22 | semidirect |
| 14. #10587505 | C22 | semidirect |
| 15. C24×C17 | C2×C4 | semidirect |
| 19. C2×Q8×C17 | C2×C4 | semidirect |
| 23. C2×D4×C17 | C2×C4 | semidirect |
| 24. C2×D4×C17 | C2×C4 | semidirect |
| 27. C22×C4×C17 | C2×C4 | semidirect |
| 28. C22×C4×C17 | C2×C4 | semidirect |
| 77. C2×#41 | Dic17 | semidirect |
| 79. C22×D4 | Dic17 | semidirect |
| 86. C17 | #2883 | semidirect |
| 87. C24 | C2×Dic17 | semidirect |
| 91. C2×Q8 | C2×Dic17 | semidirect |
| 95. C2×D4 | C2×Dic17 | semidirect |
| 96. C2×D4 | C2×Dic17 | semidirect |
| 100. C22×C4 | C2×Dic17 | semidirect |
| 101. C22×C4 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763284 | 2 |
| #11762783 | 2 |
| C2×#10587505 | 2 |
| C2×C17×H(5,𝔽2) | 2 |
| #2883 | 17 |