Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11763359 | C2 | semidirect |
| 2. #11763343 | C2 | semidirect |
| 3. #11763218 | C2 | semidirect |
| 4. #11763198 | C2 | semidirect |
| 5. #11763174 | C2 | semidirect |
| 6. #11763169 | C2 | semidirect |
| 7. #11763045 | C2 | semidirect |
| 8. #11763038 | C2 | semidirect |
| 9. #11762922 | C2 | semidirect |
| 10. #11762911 | C2 | semidirect |
| 11. C2×C17×#97 | C2 | semidirect |
| 110. C8×C17 | #41 | semidirect |
| 142. C2×#97 | D17 | semidirect |
| 180. C17 | #3180 | semidirect |
| 248. C8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763343 | 2 |
| #11763218 | 2 |
| #11763198 | 2 |
| #11763174 | 2 |
| #11763169 | 2 |
| #11763045 | 2 |
| #11763038 | 2 |
| #11762922 | 2 |
| #11762911 | 2 |
| C2×C17×#97 | 2 |
| #3180 | 17 |