Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 1. #11763836 | C2 | semidirect |
| 2. #11763826 | C2 | semidirect |
| 3. #11763777 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 9. C22×#3624 | C22 | semidirect |
| 10. C2×#63242 | C22 | semidirect |
| 18. C22⋊#3624 | C22 | semidirect |
| 19. #10587544 | C22 | semidirect |
| 20. #10587543 | C22 | semidirect |
| 21. C4×#3624 | C22 | semidirect |
| 26. C2×C22⋊D17 | C8 | semidirect |
| 47. C23×C17 | C2×C8 | semidirect |
| 52. C22×D17 | C2×C8 | semidirect |
| 58. C22⋊D17 | C2×C8 | semidirect |
| 63. C2×Dic17 | C2×C8 | semidirect |
| 117. C17 | #2972 | semidirect |
| 147. C23 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763836 | 2 |
| #11763826 | 2 |
| #11763777 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×#10587567 | 2 |
| #2972 | 17 |