Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10587533 | C4 | semidirect |
| 14. C8×#595 | C4 | semidirect |
| 15. C17×#106 | C4 | semidirect |
| 16. #10587488 | C4 | semidirect |
| 17. #10587479 | C4 | semidirect |
| 57. C8×C17 | C42 | semidirect |
| 58. #3622 | C42 | semidirect |
| 67. #595 | #106 | direct (N × H) |
| 93. #106 | #595 | direct (N × H) |
| 96. C17 | C4×#106 | semidirect |
| 137. C8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| C2×C8×#595 | 2 |
| C4⋊C4×#595 | 2 |
| #11763682 | 2 |
| #106×D17 | 2 |
| C4×#106 | 17 |