Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11763802 | C2 | semidirect |
| 4. (C2×#595)⋊Q8 | C2 | semidirect |
| 5. #11763688 | C2 | semidirect |
| 6. #11763681 | C2 | semidirect |
| 19. C17×#137 | C4 | semidirect |
| 20. #10587637 | C4 | semidirect |
| 21. #10587628 | C4 | semidirect |
| 26. #10587595 | C4 | semidirect |
| 37. C2×Q8×C17 | C2×C4 | semidirect |
| 54. C2×Dic34 | C2×C4 | semidirect |
| 71. M16×C17 | C2×C4 | semidirect |
| 76. #63223 | C2×C4 | semidirect |
| 168. #137 | #595 | semidirect |
| 186. C17 | #1882 | semidirect |
| 200. C2×Q8 | C2×#595 | semidirect |
| 221. M16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763878 | 2 |
| D17⋊#104 | 2 |
| #11763802 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763688 | 2 |
| #11763681 | 2 |
| #137×D17 | 2 |
| #1882 | 17 |