Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763415 | C2 | semidirect |
| 2. #11763186 | C2 | semidirect |
| 3. #11763175 | C2 | semidirect |
| 4. #11763063 | C2 | semidirect |
| 5. #11763046 | C2 | semidirect |
| 6. #11762920 | C2 | semidirect |
| 7. #11762891 | C2 | semidirect |
| 8. #11762763 | C2 | semidirect |
| 9. C17×#499 | C2 | semidirect |
| 82. #499 | D17 | semidirect |
| 113. C17 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763415 | 2 |
| #11763186 | 2 |
| #11763175 | 2 |
| #11763063 | 2 |
| #11763046 | 2 |
| #11762920 | 2 |
| #11762891 | 2 |
| #11762763 | 2 |
| C17×#499 | 2 |
| #3176 | 17 |