Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 12. #10587542 | C4 | semidirect |
| 13. #10587532 | C4 | semidirect |
| 14. C8×#595 | C4 | semidirect |
| 15. C17×#97 | C4 | semidirect |
| 16. #10587486 | C4 | semidirect |
| 17. #10587474 | C4 | semidirect |
| 47. #3624 | C42 | semidirect |
| 48. C8×C17 | C42 | semidirect |
| 49. #3622 | C42 | semidirect |
| 56. #595 | #97 | direct (N × H) |
| 80. #97 | #595 | direct (N × H) |
| 82. C17 | C4×#97 | semidirect |
| 114. C8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763768 | 2 |
| C2×#10587532 | 2 |
| C2×C8×#595 | 2 |
| C42×#595 | 2 |
| #97×D17 | 2 |
| C4×#97 | 17 |