Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. #11763820 | C2 | semidirect |
| 4. #11763681 | C2 | semidirect |
| 17. C17×#100 | C4 | semidirect |
| 18. #10587504 | C4 | semidirect |
| 19. #10587494 | C4 | semidirect |
| 39. M16×C17 | C2×C4 | semidirect |
| 40. #63223 | C2×C4 | semidirect |
| 112. #100 | #595 | semidirect |
| 113. C17 | #1856 | semidirect |
| 127. M16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763876 | 2 |
| #11763820 | 2 |
| #11763761 | 2 |
| #11763681 | 2 |
| #100×D17 | 2 |
| #1856 | 17 |