Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763366 | C2 | semidirect |
| 2. #11763168 | C2 | semidirect |
| 3. #11763163 | C2 | semidirect |
| 4. #11762818 | C2 | semidirect |
| 6. C4×#63223 | C2 | semidirect |
| 18. #10587556 | C22 | semidirect |
| 19. #10587555 | C22 | semidirect |
| 21. #10587506 | C22 | semidirect |
| 23. #10587474 | C22 | semidirect |
| 24. C4×#3622 | C22 | semidirect |
| 108. C17 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763168 | 2 |
| #11763163 | 2 |
| #11762818 | 2 |
| #11762814 | 2 |
| C4×#63223 | 2 |
| C2×C17×#124 | 2 |
| #3140 | 17 |