Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11763139 | C2 | semidirect |
| 3. #11763099 | C2 | semidirect |
| 4. #11763014 | C2 | semidirect |
| 6. C4×#63229 | C2 | semidirect |
| 7. #11762862 | C2 | semidirect |
| 23. #10587555 | C22 | semidirect |
| 24. #10587555 | C22 | semidirect |
| 26. C4×Dic34 | C22 | semidirect |
| 29. #10587481 | C22 | semidirect |
| 30. #10587479 | C22 | semidirect |
| 31. C4⋊#3622 | C22 | semidirect |
| 32. C4×#3622 | C22 | semidirect |
| 78. C2×C4×C17 | SD16 | semidirect |
| 145. C17 | #3101 | semidirect |
| 195. C2×C4 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763139 | 2 |
| #11763099 | 2 |
| #11763014 | 2 |
| #11762960 | 2 |
| C4×#63229 | 2 |
| #11762862 | 2 |
| C2×C4×D4×C17 | 2 |
| #3101 | 17 |