Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #11763338 | C2 | semidirect |
| 2. #11763211 | C2 | semidirect |
| 3. #11763163 | C2 | semidirect |
| 4. #11763064 | C2 | semidirect |
| 6. #11763052 | C2 | semidirect |
| 7. #11762921 | C2 | semidirect |
| 8. #11762916 | C2 | semidirect |
| 9. #11762910 | C2 | semidirect |
| 10. C4×#63218 | C2 | semidirect |
| 11. C17×#495 | C2 | semidirect |
| 108. #495 | D17 | semidirect |
| 148. C17 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763338 | 2 |
| #11763211 | 2 |
| #11763163 | 2 |
| #11763064 | 2 |
| #11763059 | 2 |
| #11763052 | 2 |
| #11762921 | 2 |
| #11762916 | 2 |
| #11762910 | 2 |
| C4×#63218 | 2 |
| C17×#495 | 2 |
| #3183 | 17 |