Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763148 | C2 | semidirect |
| 4. #11763095 | C2 | semidirect |
| 5. #11763089 | C2 | semidirect |
| 6. #11763016 | C2 | semidirect |
| 8. #11762901 | C2 | semidirect |
| 9. SD16×Dic17 | C2 | semidirect |
| 10. #11762861 | C2 | semidirect |
| 11. C17×#461 | C2 | semidirect |
| 138. #461 | D17 | semidirect |
| 179. C17 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| C4×#63254 | 2 |
| #11763148 | 2 |
| #11763095 | 2 |
| #11763089 | 2 |
| #11763016 | 2 |
| #11762968 | 2 |
| #11762901 | 2 |
| SD16×Dic17 | 2 |
| #11762861 | 2 |
| C17×#461 | 2 |
| #3107 | 17 |