Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763673 | C2 | semidirect |
| 4. #11763672 | C2 | semidirect |
| 5. #11763671 | C2 | semidirect |
| 6. #11763670 | C2 | semidirect |
| 58. C8×C17 | M16 | semidirect |
| 60. #3622 | M16 | semidirect |
| 100. C17 | #1569 | semidirect |
| 138. C8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763830 | 2 |
| #11763812 | 2 |
| #11763673 | 2 |
| #11763672 | 2 |
| #11763671 | 2 |
| #11763670 | 2 |
| M16×Dic17 | 2 |
| #1569 | 17 |