Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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. #11763687 | C2 | semidirect |
| 2. #11763653 | C2 | semidirect |
| 4. C22×D4×C17 | C4 | semidirect |
| 10. #10587502 | C4 | semidirect |
| 93. C22×D4 | #595 | semidirect |
| 99. C17 | #1343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763687 | 2 |
| #11763653 | 2 |
| #11762717 | 2 |
| #1343 | 17 |