Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 124 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. C4×#3624 | C4 | semidirect |
| 14. C4×#3624 | C4 | semidirect |
| 16. C17×C4⋊C8 | C4 | semidirect |
| 17. #10587485 | C4 | semidirect |
| 18. C4⋊#3622 | C4 | semidirect |
| 25. C4⋊#595 | C8 | semidirect |
| 57. #3624 | C4⋊C4 | semidirect |
| 68. C4×C17 | C4×C8 | semidirect |
| 72. Dic17 | C4×C8 | semidirect |
| 93. C4⋊C8 | #595 | semidirect |
| 98. C17 | C8×C4⋊C4 | semidirect |
| 151. C4 | C8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63242 | 2 |
| C2×C8×#595 | 2 |
| C4×C4⋊#595 | 2 |
| #11763674 | 2 |
| C4⋊C8×D17 | 2 |
| C8×C4⋊C4 | 17 |