Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 2. C2×#10587549 | C2 | semidirect |
| 4. (C2×#595)⋊Q8 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 18. C2×SD16×C17 | C4 | semidirect |
| 19. C2×#63230 | C4 | semidirect |
| 20. C2×#63229 | C4 | semidirect |
| 23. C2×#63219 | C4 | semidirect |
| 37. C2×Q8×C17 | C2×C4 | semidirect |
| 52. C2×Dic34 | C2×C4 | semidirect |
| 64. C2×C8×C17 | C2×C4 | semidirect |
| 67. C2×#3622 | C2×C4 | semidirect |
| 92. C2×#595 | SD16 | semidirect |
| 170. C2×SD16 | #595 | semidirect |
| 183. C17 | #1877 | semidirect |
| 191. C2×Q8 | C2×#595 | semidirect |
| 218. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| C2×#10587549 | 2 |
| C2×#10587547 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763683 | 2 |
| #11763674 | 2 |
| C2×SD16×D17 | 2 |
| #1877 | 17 |