Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763364 | C2 | semidirect |
| 3. #11763102 | C2 | semidirect |
| 4. #11763090 | C2 | semidirect |
| 5. #11763089 | C2 | semidirect |
| 6. #11763058 | C2 | semidirect |
| 7. #11763052 | C2 | semidirect |
| 8. #11763011 | C2 | semidirect |
| 9. #11763007 | C2 | semidirect |
| 10. #11762831 | C2 | semidirect |
| 11. C17×#461 | C2 | semidirect |
| 145. #461 | D17 | semidirect |
| 185. C17 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #11763356 | 2 |
| #11763102 | 2 |
| #11763090 | 2 |
| #11763089 | 2 |
| #11763058 | 2 |
| #11763052 | 2 |
| #11763011 | 2 |
| #11763007 | 2 |
| #11762831 | 2 |
| C17×#461 | 2 |
| #3254 | 17 |