Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C4⋊Q8×D17 | C2 | semidirect |
| 3. #11763213 | C2 | semidirect |
| 4. #11763154 | C2 | semidirect |
| 5. #11763124 | C2 | semidirect |
| 6. #11763121 | C2 | semidirect |
| 7. #11763090 | C2 | semidirect |
| 8. #11763089 | C2 | semidirect |
| 9. #11763086 | C2 | semidirect |
| 10. #11762861 | C2 | semidirect |
| 11. C17×#474 | C2 | semidirect |
| 145. #474 | D17 | semidirect |
| 184. C17 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763356 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763213 | 2 |
| #11763154 | 2 |
| #11763124 | 2 |
| #11763121 | 2 |
| #11763090 | 2 |
| #11763089 | 2 |
| #11763086 | 2 |
| #11762861 | 2 |
| C17×#474 | 2 |
| #3226 | 17 |