Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
374 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 80 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. C2×Q8×#595 | C2 | semidirect |
| 2. C2×#10587549 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 20. C2×SD16×C17 | C4 | semidirect |
| 21. C2×#63230 | C4 | semidirect |
| 22. C2×#63229 | C4 | semidirect |
| 25. C2×#63219 | C4 | semidirect |
| 91. C2×#595 | SD16 | semidirect |
| 93. Q8×C17 | C22⋊C4 | semidirect |
| 113. Dic34 | C22⋊C4 | semidirect |
| 168. C2×SD16 | #595 | semidirect |
| 182. C17 | #1880 | semidirect |
| 239. Q8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| C2×#10587549 | 2 |
| C2×#10587547 | 2 |
| #11763761 | 2 |
| #11763683 | 2 |
| #11763674 | 2 |
| C2×SD16×D17 | 2 |
| #1880 | 17 |