Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #11763212 | C2 | semidirect |
| 4. #11763153 | C2 | semidirect |
| 5. #11763148 | C2 | semidirect |
| 6. #11763095 | C2 | semidirect |
| 7. #11763049 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 10. #11762844 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 118. #475 | D17 | semidirect |
| 156. C17 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763533 | 2 |
| #11763532 | 2 |
| #11763212 | 2 |
| #11763153 | 2 |
| #11763148 | 2 |
| #11763095 | 2 |
| #11763049 | 2 |
| C4×#63231 | 2 |
| #11762874 | 2 |
| #11762844 | 2 |
| C17×#475 | 2 |
| #3342 | 17 |