Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11763820 | C2 | semidirect |
| 3. #11763819 | C2 | semidirect |
| 13. C2×M16×C17 | C4 | semidirect |
| 14. C2×#63223 | C4 | semidirect |
| 15. M16×D17 | C4 | semidirect |
| 17. C2×#63218 | C4 | semidirect |
| 19. #10587534 | C22 | semidirect |
| 20. #10587533 | C22 | semidirect |
| 39. M16×C17 | C2×C4 | semidirect |
| 40. C2×C8×C17 | C2×C4 | semidirect |
| 41. #63223 | C2×C4 | semidirect |
| 42. C2×#3622 | C2×C4 | semidirect |
| 43. #63218 | C2×C4 | semidirect |
| 44. C8×D17 | C2×C4 | semidirect |
| 107. C2×M16 | #595 | semidirect |
| 118. C17 | #2911 | semidirect |
| 133. M16 | C2×#595 | semidirect |
| 137. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763820 | 2 |
| #11763819 | 2 |
| C2×M16×D17 | 2 |
| #2911 | 17 |