Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 13. #10587544 | C4 | semidirect |
| 14. C4⋊#3624 | C4 | semidirect |
| 16. C4×C8×C17 | C4 | semidirect |
| 17. C8×Dic17 | C4 | semidirect |
| 18. C8×Dic17 | C4 | semidirect |
| 19. C4×#3622 | C4 | semidirect |
| 25. C4⋊#595 | C8 | direct (N × H) |
| 60. C8×C17 | C4⋊C4 | semidirect |
| 62. #3622 | C4⋊C4 | semidirect |
| 71. C4×C17 | C4×C8 | semidirect |
| 75. Dic17 | C4×C8 | semidirect |
| 100. C4×C8 | #595 | semidirect |
| 102. C17 | C8×C4⋊C4 | semidirect |
| 145. C8 | C4⋊#595 | direct (N × H) |
| 157. C4 | C8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763810 | 2 |
| C2×C8×#595 | 2 |
| C4×C4⋊#595 | 2 |
| #11763674 | 2 |
| C4×C8×D17 | 2 |
| C8×C4⋊C4 | 17 |