Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 1. #11763876 | C2 | semidirect |
| 2. #11763808 | C2 | semidirect |
| 3. #11763801 | C2 | semidirect |
| 4. #11763790 | C2 | semidirect |
| 5. #11763691 | C2 | semidirect |
| 6. #11763677 | C2 | semidirect |
| 17. C2×SD16×C17 | C4 | semidirect |
| 18. C2×#63230 | C4 | semidirect |
| 19. C2×#63228 | C4 | semidirect |
| 22. C2×D136 | C4 | semidirect |
| 29. C2×Q8×C17 | C2×C4 | semidirect |
| 42. C2×D68 | C2×C4 | semidirect |
| 59. C2×C8×C17 | C2×C4 | semidirect |
| 62. C2×#3622 | C2×C4 | semidirect |
| 141. C2×SD16 | #595 | semidirect |
| 155. C17 | #1904 | semidirect |
| 161. C2×Q8 | C2×#595 | semidirect |
| 184. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763876 | 2 |
| #11763808 | 2 |
| #11763801 | 2 |
| #11763790 | 2 |
| #11763691 | 2 |
| #11763677 | 2 |
| C2×#10587600 | 2 |
| #1904 | 17 |